2006 Activity Report - Consorzio RFX 2006 Activity Report Technical Scientific Committee 18 January...
Transcript of 2006 Activity Report - Consorzio RFX 2006 Activity Report Technical Scientific Committee 18 January...
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2006 Activity Report
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2006 Activity Report Technical Scientific Committee 18 January 2007
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CONTENTS
1. Introduction pag. 3
2 RFX-mod pag. 5
2a Systems performance and control developments
2b MHD physics and mode control
2c Transport and confinement
2d Edge phenomena
3 Theory and modeling studies pag. 37
3a Nature of the RFP dynamo
3b Active control of MHD modes
3c ITG mode study
3d Greenwald density limit
3e Pinch effect for chaotic transport
3f ORBIT update and transport in various regimes
3g Edge modeling
4 Collaboration to other experiments (RFP and Tokamak) pag. 44
4a Collaboration on MHD studies
4b Collaboration on transport studies
4c Collaboration on edge physics
5 Diagnostics pag. 50
5a Multichannel MOSS Spectrometer
5b DNBI
5c Improvement of the SXR tomographic system
5d Integrated System of Internal Sensors
6 ITER pag. 53
6a ITER Neutral Beam Injector
6b ITER diagnostics
6c ITER vertical displacement events and disruptions
6d ITER ICH Antenna
6e EU Superconducting Dipole
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7 Tokamak Engineering pag. 72
7a JET
7b FT3
7c JT-60-SA
8 Fusion Spin-offs pag. 81
8a Low power plasma source at atmospheric pressure
9 List of Collaborations pag. 82
9a Collaboration with other RFP laboratories
9b Collaborations with Tokamak laboratories
9c Collaborations on Theory
9d Other Collaborations
10 Education and information to the public pag. 83
11 List of Publications 2006 pag. 85
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1. Introduction
The program of Consorzio RFX for the year 2006 has been presented and discussed at the 17th
meeting of the RFX Technical-Scientific Committee on 8 November 2005.
The program has been approved by the Board of Directors of Consorzio RFX on 30 January
2006 and by the Steering Committee of the Euratom-ENEA Association on 20 January 2006.
The final approval of the program and of the relevant budget was given by the Consorzio
Partners on 5 May 2006.
The key objectives of the 2006 program were:
- “the exploitation of the new capabilities of the modified RFX to obtain important and
sound scientific results both in terms of confinement improvement and of active control
of MHD instabilities;
- to start giving a significant contribution to the ITER construction, with particular
reference to the Neutral Beam Injector.”
The planned experimental schedule included 36 weeks of operation and the main scientific
lines were: plasma performance optimization and active control of MHD modes.
Increase of plasma current to the MA range was planned as a fundamental step in the 2006
plan.
RFX operations ran smoothly during the whole year, confirming the excellent reliability of the
machine and of its power supplies, diagnostics, control and data acquisition system. A total of
166 experimental days have allowed producing 2.887 pulses, 2014 of them being useful for
plasma physics.
The main results are reported in Section 2; among them it is worthwhile to note the successful
operation with plasma current in the 1 MA range, owing to the much smoother plasma-wall
interaction offered by the new active MHD control system.
The saddle coil system also allowed to directly drag the internally resonant m=1 modes, so
keeping rotation for the whole pulse.
Higher current operation has also been associated with higher probability of occurrence of
beneficial Quasi-Single Helicity states.
The wide range of explored plasma regimes allowed us to analyze the scaling of the main
transport and confinement properties as a function of the basic plasma parameters. A
comparison has been possible with old RFX data, clearly demonstrating the improvements
obtained by the Virtual Shell operation; in particular, the central electron temperature now
increases nearly linearly with current, whereas it tended to saturate in RFX.
Section 3 of this report summarizes the main results of the theory and modeling studies, aimed
both to improve the understanding of basic properties of particle and energy transport, and to
support the search of optimum MHD control scenarios.
Collaborations with other fusion laboratories (Section 4) have been quantitatively reduced with
respect to previous years, but very significant results have been obtained, in particular on MST
and ASDEX UG.
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The main planned diagnostic developments have been postponed to the second part of the year,
due to the late budget approval; moreover, some technical difficulties prevented us from taking
advantage of the new diagnostic neutral beam injector; nevertheless, some important
improvements (Section 5) have been obtained in spectroscopy and tomography.
Section 6 reports about the second main task of the 2006 program: the RFX contribution to
ITER.
According to plans, almost all efforts have been dedicated to the design of the Neutral Beam
Injector and to the preparation for the construction of the relevant Test Facility in Padova.
Work has been performed under an EFDA contract, regularly closed in May; two further
contracts have been placed during the year. The various options, in particular those including
the SINGAP accelerator and the RF ion source, have been developed at the level of detailed
design studies, including thermomechanical, structural and electrostatic analysis. New
solutions have been proposed for the power supply system, validated by a feasibility
assessment in collaboration with industry.
All these activities on the NBI enforced the RFX leadership at the EU level; moreover, a
significant collaboration has been established with the Japanese partners.
During 2006, a significant amount of work has been also dedicated to design and construction
tasks for Tokamak machines (Section 7); among the results, it is worthwhile to mention the
design of the new JET Enhanced Radial Field Amplifier.
Finally, Section 8 illustrates a new spin-off of plasma research, Section 9 reports the list of
collaborations and Section 10 lists the educational activities, traditionally being a key
commitment of Consorzio RFX.
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Fig.2.1: Average magnetic field vertical component on the equatorial plane without (pulse 18871) and with (pulse 19496) feedback control in the presence of the same reference.
2 RFX-mod
2a Systems performance and control developments
2a.1 Control of plasma equilibrium In view of the exploitation of higher plasma current regimes, the action of the equilibrium
controller has been improved, in terms of control quality, robustness and reliability. In
particular, in order to optimize plasma startup and equilibrium control, a characterization of
the load assembly of RFX-mod was carried out. The high number of electromagnetic probes
mounted on the components of the load assembly allowed to analyze the response to a variation
of the magnetic field vertical component of the three toroidal conducting structures (vacuum
vessel, shell and mechanical structure), whose eddy currents affect the plasma equilibrium
magnetic configuration. The analysis led to the design and implementation of the feedback
control system of the magnetic field vertical component before gas ionization and allowed
meeting the requirement of an accurate control independently of the magnetizing winding
programming [Marchiori06a]. Fig. 2.1 illustrates the average vertical field component on the
equatorial plane achieved before the plasma rise with and without feedback control in pulses
19496 and 18871, respectively.
To minimize the plasma position steady-state error, the controller was completed with an
integral action that was successfully commissioned and routinely used in the successive
experimental campaigns. To increase robustness and reliability of the system, a set of activities
was carried out, including:
- Development of a dedicated protection system against vertical and radial overstresses on
the field shaping coils and of an independent back-up, real-time application to check and
limit overstresses, whose aim is to enhance the protection reliability;
- Implementation of controlled ramp-down of the references of the field shaping amplifiers in
case of protection request either generated internally or originating from the Machine Fast
Protection System (SGPR);
- Development of a protection to avoid
overdriving the field shaping power
amplifiers and windings in case of
failure of the input measurements;
- Development of a protection to prevent
a drastic reaction, such as Full Poloidal
Shutdown, in case of reversal failure;
- Limitation of voltage reference
derivatives to avoid voltage unbalance
on the field shaping power amplifiers,
resulting in a shutdown request;
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Fig. 2.2: Generation of m=1 n=-7 mode. Magnetic field spectra obtained without (yellow) and with decoupling (solid).
- Introduction of a dead-band for the plasma current where the control is inactive, in order
to avoid intervention of the system in the first period of the discharge, where the shell
passive action is predominant.
Some minor issues concerning equilibrium control still remain open, such as, for instance,
filtering of the currents to avoid ripple propagation to the references and the development of a
non-linear, anti-windup scheme to avoid excessive control delay due to the integral action.
2a.2 Control of MHD modes A significant effort was devoted in 2006 to the development and validation of models for MHD
mode control and in their experimental testing.
First of all, an electromagnetic model of the active system was developed, taking into account
the toroidal geometry and the effects of passive structures. The model parameters were
estimated by processing experimental data collected in dedicated measurement campaigns.
State space representations were adopted to describe the dynamics of the active saddle coil
currents and the fluxes measured by saddle probes. Open and closed loop responses were
computed and compared with experimental data. Through this model a static matrix M was
obtained accounting for the mutual coupling among saddle coils and among saddle coils and
sensors [Marchiori06b]. Fig. 2.2 shows, as an example, by yellow bars the measured normalized
amplitudes of magnetic field modes when the system is used to generate in closed loop only the
m=1 n=-7 mode. In mode generation, no decoupling is used among coils. In this case, due to
toroidal geometry, the achieved magnetic
field spectrum shows the presence of two
spurious modes, the m=0 n=7 and m=2 n=7
ones, with noticeable amplitudes. The
spectrum is displayed in solid bars when the
generation is performed using the decoupling
block. As shown in the figure, the achieved
spurious mode suppression is very effective.
An m=0 n=7 component arises in the current
spectrum when using the decoupling block to
cancel the m=0 n=7 radial field mode. A
further tuning of the model was carried out
to improve its accuracy in reproducing the
magnetic field diffusion into the load assembly.
Significant work was also devoted to the optimization of the Virtual Shell (VS) control scheme. The power amplifiers and saddle coils were commissioned up to nominal current (400 A) and
control was applied routinely to achieve stabilization of resistive wall modes (RWMs), to induce
reproducible plasma rotation and to cancel the resistive kink tearing modes (TMs) at the sensor
radius [Bolzonella06].
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Fig. 2.3: Feedback control on RWMs. Comparison among pulses programmed with same parameters, but differing in RWM control.
Fig. 2.4:Power consumption associated to MHD mode control.
TM activity appears also reduced in the plasma core, as confirmed by magnetic measurements
and SXR double filter diagnostics. TM rotation was routinely achieved byapplying the VS
scheme, significantly contributing to the
alleviation of plasma wall interaction and
allowing, so far, the increase of plasma
current up to 1MA. Experimental
campaigns are in progress to reach full
design performances. The control of the
radial field boundary allowed executing
well controlled plasma pulses up to 360
ms, corresponding to six shell time
constants, far beyond the original design
value of 250 ms. Fig. 2.3 illustrates the
flexibility achieved in the cooperation of
the MHD mode control, comparing three
pulses programmed with the same parameters (the m=1 n=-6 being the most unstable RWM),
but differing in how RWMs are controlled.
Pulse #17301 (blue) is executed excluding
m=1 n=-6 to n=-3 RWMs from control.
The m=1 n=-6 unstable mode grows and
when its amplitude reaches a few mT the
pulse is early terminated. Pulse #17287
(red) is executed with full VS control
(except, as usually, for the m=1 n=0
equilibrium field). The amplitude of the
m=1 n=-6 mode is kept at negligible
values and the plasma current is well
sustained up to 250 ms. Pulse #17304
(green) is executed letting the m=1 n=-3
to n=-6 free to grow until t=150ms and at
this point control is applied on the modes
so promptly reducing mode amplitude (in
~10ms) to very low values.
To quantify the power needed in RFX-
mod for mode control, fig. 2.4 shows the
power supplied by the power amplifiers to
control the MHD modes by means of VS
in pulse #19648 at 1 MA. In this pulse the references for the m=1 n=-7, -8, -10, -11, -12 TM are
not preset to cancel the modes, but to produce rotating modes. The figure shows, from top to
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Fig. 2.6: Simulation of system response in terms of toroidal field at the wall.
Fig. 2.5: Block diagram of Mode Control.
bottom, the plasma current, the power
supplied by the amplifiers for MHD mode
control, the ohmic power associated with the
plasma, and the m=1 spectrum at flat-top,
respectively. During the flat-top the power
needed to control the MHD mode is ~1% of
the plasma ohmic power [Luchetta06].
Another important task was the
development of advanced control schemes,
such as the Closer Virtual Shell and the Mode Control with and without sideband suppression.
The Closer Virtual Shell algorithm computes the field distribution in the region between the plasma and the sensors and aims at creating a VS beyond the sensor radius. This technique, currently being experimented, can force the magnetic boundary at any radius in the vacuum region between the last closed flux surface and the active coils.
Direct Mode Control was implemented introducing a derivative control to compensate for the radial field penetration delay due to the passive structure. As the delay depends on the mode
number, it was not straightforward to model the compensation in the VS. Fig. 2.5 displays the
block diagram of MC. The main difference with VS is that the regulators act directly on the harmonic components. To smooth the derivative action, a filter (1-pole Butterworth) is applied
to the mode components.
Attention was also paid to sideband suppression, as the discrete coil system intrinsically
produces magnetic field sidebands at
the sensors. These spurious
components add to the mode signals
and are seen by the control system as
spatial aliasing. A model was
developed and implemented to
compute the sidebands and to clean
the vertical field mode signals. The
development and the optimization of
these advanced control schemes is
still ongoing and will continue during
2007.
2a.3 Control of Toroidal field The toroidal power amplifiers and
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windings were commissioned up to 12 and 5 kA of direct and reverse currents, respectively.
Various control schemes were developed and tested, among which the control of m = 0 modes
and the feedforward control of the reversal parameter F and of the safety factor q at the edge. A
new feedback control system of the toroidal field at the wall was also designed on the basis of a
dynamic model which accounts for the closed loop response of the toroidal winding current
during the flat-top and the perturbation due the vessel poloidal current. In figure 2.6 a
simulation of the system response in terms of toroidal field at the wall and inverter current
reference is shown in the case of a field reference step variation. The desired value is achieved
within 20 ms, while the limit inverter current reference is reached for a very short time. The
system capability to compensate for field perturbations due to poloidal loop voltage variations
is also shown in the simulation. The effect of 2 V step variation of the poloidal loop voltage is
cancelled again within 20 ms.
An extension to the feedback control of F was studied in view of more advanced operation
scenarios in which simultaneous control of F and Theta parameters could be implemented. The
commissioning and experimental tests of this new system are expected in the next months.
2b MHD physics and mode control
Following the highly successful initial Virtual Shell (VS) experiments of 2005, active MHD
control studies continued also in 2006 on RFX-mod. On the one hand very effective rotation
schemes were developed, which allowed safe and successful extension of the plasma current
range up to 1.1 MA. On the other hand, several advanced RFP scenarios were also studied in
more detail. QHS studies entailed both the analysis of the “spontaneous” and “stimulated”
state transitions, Oscillating Poloidal Current Drive (OPCD) experiments were extended up to
1MA, Self-Similar Current Decay (SSCD) scenarios were explored in more detail. Studies on
Oscillating Field Current Drive (OFCD) and RWM control continued and will also be briefly
outlined in the following sections.
2b.1 Mode rotation and 1MA pulses In RFX the lack of control of radial fields at the plasma boundary hindered operation at high
current. Nearly 50% of pulses at Ip > 0.9 MA suffered “fast” terminations and most of the
remaining ones showed carbon blooms due to highly localized Plasma Wall Interaction (PWI)
[Bartiromo00]. In those conditions some relief was found by Oscillating Poloidal Current Drive
(OPCD) [Bolzonella01] or rotating the locked mode (LM) by Rotating Toroidal Field Modulation
(RTFM) [Bartiromo99].
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Conversely, the improved materials and magnetic boundary of RFX-mod VS [Zanca06a,
Paccagnella06] allow performing long and well controlled 1 MA pulses [Ortolani06], where the
on axis loop voltage is in the range 20÷30 V, compared to the 30÷50 V of RFX pulses at the
same current (Fig. 2.7). The temperature and the confinement time are also higher with a
positive current scaling, which, contrary to the past, does not show any saturation at 1 MA
[Innocente06], leading to τE ∼1.5 ms. Nonetheless, the incomplete field error correction by the
saddle coils still causes the PWI to concentrate in the region of the LM. This results in a rapid
deterioration of the wall conditioning, which
calls for frequent sessions of H and He GDC.
A solution to this problem is to spread power
deposition around the torus by externally
inducing the rotation of the MHD modes. To
this end, RTFM can be used also in RFX-mod.
The LM is rotated around the torus at 10÷20
Hz by applying an m = 0 n = 1 mode of a few
mT in terms of Br(a). Unfortunately, although
such values are lower than those needed in the
past, in RFX-mod with VS they cause an
increase of a few volts of the loop voltage. This is explained by considering that the largest
residual deformation of the edge magnetic surface with VS is due to the m = 0 component
[Martini06]. Hence, even the small additional error due to RTFM gives a non-negligible
contribution to localized PWI.
On the other hand, we developed several new schemes for the rotation of internally resonant m
= 1 modes by rotating m = 1 perturbations applied via
the saddle coils. They take advantage of the direct
coupling of each perturbation with the homologous
mode, which occurs at the corresponding resonant
surface. We used both Mode Control (MC) with complex
gains and VS + rotating perturbation schemes
[Luchetta06]. The MC + complex gains applies a
spatially out-of-phase correction to each mode, thus
applying a torque that can be increased by increasing
(in modulus) the phase of the complex gain. Of course
the larger is such a phase, the higher is the residual
field error, because of the incomplete correction. The
scheme results in a rotation frequency of the order of
10÷20 Hz. In the VS + rotating perturbation schemes
the applied torque on each mode is proportional to the
toroidal angle (deg)
polo
idal
ang
le (d
eg)
18840
0
60
120
180
240
300
360
0 60 120 180 240 300 360
18741
0
60
120
180
240
300
360
toroidal angle (deg)
polo
idal
ang
le (d
eg)
18840
0
60
120
180
240
300
360
0 60 120 180 240 300 360
18741
0
60
120
180
240
300
360
Fig. 2.8: Footprint of LM maxima with active rotation: with MC + complex gains (top); with VS + rotating perturbations (bottom, path of an m=1 n=7 mode in red).
10
20
30
40
50
60
70
80
0 5 10 15
RFX
RFX-mod
Power (RFX)
Power (RFX-mod)
Vφ (0) [V]
I/N·10-14 (Am)10
20
30
40
50
60
70
80
0 5 10 15
RFX
RFX-mod
Power (RFX)
Power (RFX-mod)
Vφ (0) [V]
I/N·10-14 (Am)Fig. 2.7: On axis toroidal loop voltage vs I/N in RFX and RFX-mod pulses at ≈ 1 MA
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applied perturbation. We found that a Br(a) perturbation smaller than 0.5 mT, i.e. comparable
to the VS residual error, is adequate for mode
rotation at frequency up to 40 Hz.
Both techniques are very effective, with some
important differences. The complex gains
scheme works with somewhat smaller field
errors at the expense of a rotation velocity
which “adjusts” itself to the plasma conditions.
The latter feature is a drawback for LM
rotation at high current. In fact when the
complex gain is applied to several modes,
because of their non-linear coupling, they all
rotate at the same frequency. This results in a
“poloidal rotation” of the LM (Fig. 2.8), which
does not accomplish the desired toroidal
spreading of the localized power load.
A more effective LM rotation is obtained via
the VS + rotating perturbations schemes,
which allow controlling the mode-mode relative
phases.
The best results are obtained rotating
several modes with frequencies equally-
spaced according to their n-number (e.g. n=-8
at 10 Hz, -9 at 20 Hz, -10 at 30 Hz and so on).
The initial phase of each mode is set equal to
the one present in the plasma (computed in
real-time). In this way the modes are hooked
up in the shortest possible time, their
relative phases are maintained and the
interference pattern of the LM is helically
dragged along the path of a stationary m=1
mode (n= -7 in the case of Fig.2.8). Moreover,
thanks to the combined non-linear coupling, the m=1 modes apply a rotating torque on the m=0
n=1 mode, which responds with occasional large toroidal “jumps” not normally seen in standard
VS pulses.
The effectiveness of such LM rotation scheme is highlighted in Fig. 2.9, where 8 pulses with
plasma current larger than 1 MA and lasting over 0.35 s are superimposed. As a result of a
steady LM rotation, density control is maintained pulse after pulse and plasma performance is
0
100
200
300
400
500
600
700
800
-0,5 -0,4 -0,3 -0,2 -0,1 0,0 0,1 0,2 0,3 0,4 0,5
ensemble av. 1 MAfit 1MA19531 OPCD t=0,095 s
Te (eV)
r (m)Fig.2.10: Te profile at 1 MA with VS + rotating perturbation (ensemble average of Fig.2.9 pulses) and with OPCD (pulse 19531)
0200400600800
10001200
0 0,1 0,2 0,3 0,4
0
1020
30
4050
0 0,1 0,2 0,3 0,4
0
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0100200300400500600
0 0,1 0,2 0,3 0,4
-1200
-700
-200
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800
0 0,1 0,2 0,3 0,4
1967619669196781969919700197011970219761φ
LM (d
eg)
Τe (e
V)
n e ·1
019(m
-3)
Vφ(V
)Ι p
(kA
)
Start of controlled run down
a
b
c
d
e
t (s)
0200400600800
10001200
0 0,1 0,2 0,3 0,4
0
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4050
0 0,1 0,2 0,3 0,4
0
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0100200300400500600
0 0,1 0,2 0,3 0,4
-1200
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0 0,1 0,2 0,3 0,4
1967619669196781969919700197011970219761φ
LM (d
eg)
Τe (e
V)
n e ·1
019(m
-3)
Vφ(V
)Ι p
(kA
)
Start of controlled run down
a
b
c
d
e
t (s)Fig. 2.9: Superposition of 8 VS + rotating perturbation 1 MA pulses: a) plasma current; b) loop voltage; c) line average ne; d) central Te; e) LM toroidal angle.
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very reproducible both in terms of plasma current, loop voltage, electron density and
temperature. The Te profiles are also very similar and broad (Fig. 2.10) with central values of
400 eV.
2b.2 QSH states 2b.2.1 Spontaneous QSH studies
The new magnetic feedback system available in RFX-mod has radically influenced the MHD
phenomenology with respect to what previously studied in RFX. This had significant effects
also on the transition to Quasi-Single Helicity (QSH) states, both in terms of reproducibility
and performance.
In particular, the Virtual Shell (VS) control
scheme has been proved to be highly beneficial
for the spontaneous transition to QSH
[Piovesan06]. The smoother magnetic boundary
obtained with VS operation allows to reach
purer and more frequent QSH spectra, generally
characterized by improved duration and thermal
energy content. Such transitions to QSH exhibit
either a quasi-stationary or an intermittent
dynamics. The intermittent, sawtooth-like
dynamics, typical for example of the MST
discharges, is observed for the first time in RFX-
mod and only during VS operation.
The dynamics and duration of the QSH states in
the VS scenario is clearly correlated with plasma parameters like plasma current and magnetic
equilibrium. In particular high-current operation tends to favour longer, quasi-stationary QSH
states, as shown in Fig. 2.11. High plasma current also increases the QSH transition
probability. These observations are very promising for the next future experiments in RFX-mod
at plasma currents towards 2MA.
The soft x-ray (SXR) tomographic diagnostic installed in the RFX-mod device [Franz01] allows
characterizing the SXR emissivity with high spatial resolution (78 lines of sight spanning an
entire poloidal cross-section) and with a frequency bandwidth of several kHz. The 2D
emissivity maps obtained with tomographic algorithms permit to study in detail the plasma
dynamics in different operational scenarios. In particular, a highly emissive island region is
observed in the plasma core during QSH states, which corresponds to the helical flux surfaces
associated with the dominant mode in the magnetic spectrum.
Fig.2.11: QSH duration as a function of QSH probability for a large database of RFX-mod Virtual-Shell discharges at different plasma current.
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Similar structures are also observed during mode control experiments. In these cases the
reconstructed emissivity is an important tool for determining whether the imposed rotation of
the magnetic field at the edge is
followed by rotation of the mode inside
the plasma. Such a correspondence is
shown in Fig. 2.12. Here the poloidal
position of the island computed from
edge magnetic and internal SXR
measurements are compared and a
good match is found confirming that
the external action has a
corresponding effect in the plasma
core.
Internal reconstructions of the
magnetic flux surfaces based on soft x-
ray tomography, Thomson scattering
and ORBIT modelling have also shown
that a helical core with good confinement properties is sometimes
associated also with magnetic spectra
being apparently in the Multiple
Helicity state, based on external magnetic measurements. This is explained by the fact that the
resonant radius of the m=1,n=-7 mode, which dominates the spectrum during QSH, is very
close to the magnetic axis, in a region with low magnetic shear.
The availability of a higher spatial resolution (7mm) Thomson scattering diagnostic allows to
characterize with high detail the electron temperature profiles during QSH states. Moreover,
when the diagnostic is absolutely calibrated, also the electron density profile can be measured,
with enough accuracy to open new perspectives in the study of thermal islands. In particular
the Thomson scattering diagnostic has shown that the intermittent QSH states are associated
with the most reduced core heat diffusivity. In fact, as will be shown even clearer in Sect. 2c.4,
a further tenfold reduction of the electron heat diffusivity, which reaches values χe≈100m2s, is
measured in the QSH island region. As expected from this analysis, also the electron energy
confinement time is enhanced accordingly up to 0.8ms [Innocente06].
An increased QSH probability transition is registered during inductive profile control through
oscillating poloidal or oscillating field current drive (OPCD and OFCD) techniques. These QSH
plasmas are characterized by even further improved confinement characteristics: the island
radial width increases up to 25cm, the electron temperature inside the island reaches values of
700eV, with a radial gradient comparable to the edge gradient.
Fig. 2.12: Angular position of the magnetic island and of the center of mass of the SXR emissivity: the magnetic phase rotation is externally induced in a VS scenario. The SXR reconstructions at two different instants confirm the island rotation at the tomography section.
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These same island structures are also observed by the SXR diagnostic, which allows following
in time their dynamics. In the OPCD anti-dynamo phase, the MH state is mainly re-
established, even if sometimes a residual structure is maintained, due to the residual radial
component of the dominant magnetic mode: the high spatial resolution of the SXR tomography
allows reconstructing the SXR asymmetries associated to the residual component of the
magnetic island.
In the OPCD scenario, the 2-D reconstructed maps have been also compared with the signals
from the new multifoil diagnostic [Bonomo06] to estimate electron temperature profiles over
the low field side of the RFX-mod chamber. In correspondence to the localized SXR structures,
the electron temperature profiles show an evident asymmetry (see Fig. 2.13) similar to the
Thomson scattering measurement, with the SXR structures being characterized by a higher
temperature than the plasma nearby. Further analysis will be done in order to characterize
also with this diagnostic the temperature inside the islands.
2b.2.2 Active control of internal resistive MHD modes
The flexibility of the new MHD controlsystem allows specifying different feedback laws for the
various helicities (Selective Virtual Shell, SVS). This flexibility has been used to perform
experiments [Marrelli06] aimed at studying the effect of different boundary conditions on the
dominant resonant modes (m = 1, n = -7, -8, -9, -10) and in particular at investigating the
possibility of stimulating the onset of Quasi Single Helicity spectra. Experiments have been
performed on 600 kA and 800 kA discharge. In Selective Virtual Shell the radial field of every
harmonics resolved by the sensor coils can be independently controlled: in particular, in a first
set of experiments (“natural evolution”) control on selected helicities has been inhibited; other
experiments have been performed by assigning a non zero reference value for selected
helicities.
In natural evolution experiments, for helicities m = 1; n = -7,…, n = -10, corresponding to the
most unstable tearing modes, both the toroidal and the radial component of the field grow.
Similarly to what happens in spontaneous transition to QSH, the increase of the dominant
Fig 2.13 (a) Electron temperature (Te) profile from the new multifoil diagnostic (p is the impact parameter): the localized Te increase in the plasma core is due to the presence of a more emissive SXR structure emerging in the plasma core, as illustrated in (b).
(a) (b)
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2006 Activity Report Technical Scientific Committee 18 January 2007
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mode occurs simultaneously with a decrease of secondary modes. The drawback of this
technique is that discharge duration is systematically shorter than the reference one, as the
increase of the radial component implies a considerable non axisymmetric shift of the last
plasma surface. In “non-zero reference value” experiments, the amplitude and phase of the
radial component of a selected mode has been feedback controlled: values up to 3-4 mT have
been tested. In this scenario the discharge duration is comparable to reference SVS discharges.
The measured amplitudes of the harmonics reproducibly follow the reference value with a time
delay of the order of 5-10ms: the feedback system compensates, in fact, the different wall
penetration time of the various harmonics. When the plasma is present, the harmonics of the
applied field (obtained from the measured currents flowing into the control coils by a dynamic
model that takes into account the mutual inductances between saddle and sensor coils
[Marchiori06b]) are out of phase compared to the measured radial field harmonics: as long as
the reference value of the field is below the value it would reach without control, the externally
applied field is opposed to the one produced by the plasma. An example is shown in Fig. 2.14,
where the non-zero reference value for mode n = -7 started before discharge breakdown. In the
first phase, when no plasma is present (t < 0), the model reconstructed applied field coincide
with the measurement (both in amplitude and phase): i.e. the field is produced by the saddle
coils only. When the plasma is present (t > 0), the phase of the control harmonic switches to π
in order to apply a field opposed to the plasma generated one.
The radial component amplitude and phase can be well
controlled: in particular the phase of the plasma mode
(both radial and toroidal components) follows the
reference phase, and SXR islands locations are aligned
with the magnetic islands O-point. Given the evidence
that the phase of the plasma mode can be controlled, in a
subsequent set of experiments, the reference phase of a
selected mode was linearly varied in time. It is found
that rotations of the m = 1, n = -7 phase up to 20Hz can
be obtained. Both the radial and the toroidal component
phases rotate and intermittent SXR structures
(indicating the presence of a core helical structure) are
observed, when the magnetic spectrum displays a
transition to a QSH state. In particular, for the first time
in RFX, the thermal structures appeared at different
poloidal locations for different times in the same
discharge.
0 50 100 150 200 250 3000.00.51.01.52.02.5
b r-7
(m
T)
ReferenceMeasuredExternally applied
a)
# 17511
0 50 100 150 200 250 300
-3
-2
-1
0
phas
e (r
ad)
b)
0 50 100 150 200 250 300t (ms)
0123456
b φ(m
T)
n= -7n= -8n= -9n= -10
c)
Fig. 2.14: Time evolution of the (1,-7)mode. a) amplitude, b) phase for reference, measured and external field. c) Toroidal harmonics for the same shot.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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2b.3 Oscillating Polidal Current Drive experiments OPCD had been first tested on RFX [Bolzonella01]. It proved the possibility of improving
plasma confinement in steady state (oscillating) by the reduction of dynamo modes via
inductive poloidal current drive. In RFX it showed a positive scaling with plasma current and a
contribution to the improvement of plasma performance was also given by the periodic
mitigation of localized PWI. The latter effect is less important in RFX-mod with VS, because of
the improved magnetic boundary, therefore the confinement increase is not very large at low
currents. Conversely, a recent set of experiments at 1MA shows that OPCD in conjunction with
VS sistematically induces QSH states by reducing the amplitude of secondary dynamo modes.
Such reduction of secondary modes was clearly identified as the underlying cause for
confinement improvements resulting in central Te increases of 30%, with the onset of a temperature
gradient also in the plasma core (Fig. 2.10 e 2.15).
Detailed analyses of OPCD experiments highlighted
several interesting features, such as the decrease of
magnetic and density fluctuations during the co-
dynamo phase: another signature of the transport
improvement obtained with this technique.
2b.4 Self-Similar Current Decay experiments The Self-Similar Current Decay (SSCD) has been suggested as an interesting operation mode
for the RFP. The concept is that the dynamo should be “switched off” when the magnetic field is
forced to decay with suitable rate at fixed radial profile.
Numerical simulations predict a decrease of mode
amplitude and stochasticity. More experimental test of
SSCD have been performed in RFX-mod in 2006
[Zanca06b]. A regime, characterized by transient states
close to the m=1, n=-7 single helicity, establishes. The
magnetic regime induced by SSCD results in a 50÷100%
increase of the energy confinement time, as shown in Fig.
2.16.
2b.5 Oscillating Field Current Drive experiments The OFCD technique aims at stimulating a plasma response by oscillating poloidal and
toroidal magnetic fields at the plasma surface. Due to the plasma non linear response to these
oscillations, OFCD actively interacts with the RFP dynamo mechanism and this can result in
net drive of toroidal plasma current. In this way, OFCD can add the perspective of non
inductive current drive to the beneficial effects on confinement of pure OPCD operations.
0
0,5
1
1,5
2
2,5
3
50 60 70 80
τE
SSCDstart
t (ms)0
0,5
1
1,5
2
2,5
3
50 60 70 80
τE
SSCDstart
t (ms)Fig. 2.16: τΕ during SSCD at 600 kA (ensemble average).
Fig. 2.15: Te profile at maximum co-dynamo (red) and counter-dynamo (blue) OPCD cycle.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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The first task of 2006 OFCD operation was the integration of the technique with full virtual
shell operation. This allowed the application of OFCD to Ip≈0.8 MA plasma discharges of ≈250
ms duration and more than 100 ms of well-controlled flat-top. Having long discharges is a key
issue, since it allows summing the effect of many cycles of operation. On this kind of plasmas
the present capabilities of the toroidal and poloidal power supply systems were tested in terms
of attainable amplitudes, frequencies and relative phasing.
As an example, in Fig. 2.17 the result of a set of 100 Hz experiments is shown: keeping
constant the timing of the toroidal field oscillations (poloidal loop voltage, third frame), the
initial phase of the magnetising system (toroidal loop voltage, second frame) is changed. The
resulting toroidal flux (first frame) is then analysed for the different relative phasing. It is
interesting also to note how the resulting amplitude of the toroidal loop voltage oscillations at
the plasma edge changes with phase as a result of the interaction between the two systems,
despite the same oscillating amplitude is pre-programmed on the toroidal and poloidal coils.
First tests of periodical non-sinusoidal oscillations (e.g. square or sawtooth-like waves) were
also performed, with the aim of studying the effect of many harmonics penetrating with
different characteristic times. Further developments of OFCD will be pursued in 2007.
2b.6 Stabilization of RWMs Studies on Resistive Wall Mode (RWM) physics and their active control continued in 2006 with
particular attention to the characterisation of the instability spectra for different plasma
equilibria (i.e. for different values of the reversal parameter F), and to the study of new control
techniques, especially those of common interest for RFP and tokamak configurations.
Fig. 2.17: Example of phase scan for oscillations of about ± 12 V in the toroidal loop voltage (second window) and 6 V in the poloidal loop voltage (third window) for 100 Hz experiments. Resulting toroidal flux is shown in the first window. Black (18904): reference; red (18931): δ≈0; blue (18937): δ ≈π/4; cyan (18939): δ ≈-π/2; grey (18912): δ ≈π/2.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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Part of the first point was also the study of the plasma response to pre-programmed field
errors, the so-called resonant field amplification or RFA. This subject is particularly important
since it allows studying the effect of small, but unavoidable, magnetic field inhomogeneities on
RWM destabilisation. The flexibility of the new active control system allowed the creation of
static and rotating error fields with different amplitude and phase, and the characterisation of
stable, unstable and metastable (or marginally stable) modes for different plasma equlibria.
The RFA experiments have been carried
out in collaboration with the MPG-IPP
group in Garching (Germany). The
effectiveness of the control system on
events happening in the middle of a
plasma discharge can be tested in
experiments like the one presented in
figure 2.18. One unstable RWM is on
purpose not controlled between t=80 ms
and t=150 ms reaching in this way a
small amplitude (0.5 mT for the
experiment shown). After t=150 ms the
control on the RWM is turned on again
and in a very short time (∆t
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2006 Activity Report Technical Scientific Committee 18 January 2007
- 19 -
pick-up coils is filtered (25 point median
algorithm); the output is able to cancel the
slow m=0 dynamics: the actuators in fact are
the 12 sectors of the toroidal power supply. In
this type of experiments, the m=0 control has
been added to a standard, Virtual Shell
discharge. Results are encouraging: the total
m=0 Bt fluctuation amplitude has been
decreased (Fig. 2.19), and indications of a
decreased plasma-wall interaction have been
obtained. In fact, it seems that the control of
the m=0 modes is crucial in the startup phase of the
discharge, when the toroidal Bt field is reversed, and
the plasma-wall interaction is larger.
2b.8 Reversed Field Tokamak The underlying idea of the Reversed Field Tokamak
(RFT) operation is to first form a quasi-stationary
tokamak, and then make the transition to a RFP by
raising the loop voltage and reversing the toroidal field
at the wall. The foreseen advantage would be to start
from a relatively hot tokamak plasma, thus possibly
obtaining a better RFP state. Transiently, a new
configuration with on axis q ~1 and reversed edge q
should be formed.
During 2006, the completion of the commissioning of
the toroidal field system brought the available
maximum toroidal field up to 0.5 T. Therefore, the
formation of a tokamak-like plasma, with low loop
voltage (~ 3 V) and plasma current IΦ of about 80 kA,
which corresponds to q(a)∼3, was successfully
achieved (Fig. 2.20), using only the flat top power
supplies for all the discharge phases (including
breakdown). During the almost stationary tokamak
phase of the discharges the growth of a low
frequency instability, typically characterized by m=3
mode number, has been observed by analysing the
magnetic signals of the ISIS system (Fig.2.21), and
also fast intense magnetic activity, associated to negative spikes in the loop voltage.
Fig. 2.19: Example of feedback control of m=0 modes: in the controlled discharge, the total fluctuation amplitude of the m=0 modes is reduced (blue line) with respect to the standard, Virtual Shell discharge (red line).
Fig. 2.21: Spectrogram of a Br signal from the ISIS system, showing the development of a m=3 mode.
Fig. 2.20: Typical plasma current IΦ, loop voltage Vt(a) and q(a) signals for a RFT discharge. The attempt of transition from the tokamak to the RFP configuration starts at about 60 ms, in this case (shot #20737).
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2006 Activity Report Technical Scientific Committee 18 January 2007
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In the first attempts of transition to the RFP, a reversed configuration was not obtained, but a
minimum q(a) close to 0.3 has been reached, without suffering major disruptions during the
development of the m/n=1/1 kink mode in correspondence of a q(a)=1 condition. A preliminary
scan on different relative temporizations, between the increase of the plasma current and the
decrease of the toroidal magnetic field at the wall, has shown that this is a crucial aspect in
order to reach a final RFP configuration, along with the achievement of a correct feedback
control of the horizontal shift by means of the
vertical field coils system.
2c Transport and confinement
To study confinement properties, a large
database has been realised using all RFX and
RFX-mod shots. To improve the analysis, kinetic
quantities have been included in the database
only if measured with small errors and profile
measurements have been used where possible.
Electron temperature profiles are computed by
fitting Thomson Scattering multipoint
measurements [Alfier06b] by a two-parameter
temperature profile Te(r)=Teo(1-rα). Electron density profiles are computed by inverting the multi-chord interferometer measurements. To account for hollow density profiles, we use a four
parameter density profile ne(r)=neo-(neo-ne1-nea)rα-ne1rβ [Gregoratto98]. Ion temperature was deduced by Doppler broadening of OVII lines when available.
Poloidal beta (βp) (which in RFPs is about 50% higher than the volume average beta) and
energy confinement time (τE) are computed by integrating temperature and electron density
profiles. To increase the number of data-points the confinement analysis has been performed
assuming Ti=Te because after wall boronization the OVII line emission is blended with Boron
lines and the measurements of Ti became very uncertain. The Ti=Te assumption has been
verified by comparing Ti with Te, when both are available. Fig. 2.22 shows that the two
temperatures are approximately equal, with higher Ti at lower temperature and lower at
higher temperature. The assumption Ti=Te is hence justified at intermediate temperatures
while it is conservative at low T. On the other hand, at high temperatures Ti measurements are
affected from uncertainty in evaluating the OVII radial position, which gives a systematic
underestimation of Ti. The measurements of Ti with a neutral beam, recently installed on
RFX-mod, will allow more precise evaluations in the near future.
100
150
200
250
300
100 150 200 250 300
RFX-mod VS
T i(0
) (eV
)
Te(0) (eV)
Fig. 2.22: Central ion temperature versus central electron temperature.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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The experiments explored a large range in most of
the operational parameters, with plasma current in
the range Ip=0.1÷1 MA and density in the range
ne=0.5÷6·1019 m-3. In Fig. 2.23 Ip/N (N=πa2 is the line density) and q(a) obtained at the different
plasma currents Ip are shown for three RFX
operation modes: RFX, RFX-mod NVS and RFX-
mod VS. The figure shows that RFX-mod operates
typically at a higher Ip/N parameter than the old
RFX, in particular at currents over 800 kA the
highest Ip/N are only obtained by RFX-mod. Finally,
in RFX-mod currents over 600 kA are only explored
in VS mode, to avoid first wall damage.
2c.1 Confinement properties The values of βp and τE obtained for the three RFX
experimental conditions are drawn in Fig. 2.24.
Figure 2.24a shows that βp varies from 2% to 15%,
it is similar for both RFX-mod operation modes and is slightly higher than that of the thick
shell RFX. Finally, it clearly depends on the Ip/N parameter. Figure 2.24b shows that τE can
reach values up to 1.5 ms in RFX-mod, it is on average 50% higher for the VS operation
compared to RFX and about twice than the RFX-mod NVS operation. Energy confinement time
of RFX-mod steadily increases with plasma current while in RFX it showed a maximum at
about 600÷800 kA.
A quantitative comparison of the performance in the three experimental conditions is obtained
by averaging βp and τE of stationary discharges (low dIp/dt) in a small parameter range.
Selecting the interval Ip=550÷600 kA, Ip/N=3.5÷4.0⋅10-14 Am and F=-0.25÷-0.05, we obtained
0
5
10
15RFX-mod VSRFX-mod NVSRFX
I p/N
(Am
*10-
14)
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 200 400 600 800 1000
q(a)
Ip (kA)
Fig. 2.23: Operational range in the (Ip,I/N) and (Ip,q(a)) parameters for RFX, RFX-mod standard operation (NVS) and RFX-mod with
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 200 400 600 800 1000
RFX-mod VSRFX-mod NVSRFX
τ E (m
s)
Ip (kA)
(b)
0
2
4
6
8
10
12
14
0 5 10 15
RFX-mod VSRFX-mod NVSRFX
β p (%
)
Ip/N (Am*10-14)
(a)
Fig. 2.24: Poloidal beta and energy confinement time for the three RFX experimental conditions.
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2006 Activity Report Technical Scientific Committee 18 January 2007
- 22 -
=3.4 %, NVS=4 % and VS=4.6 % for poloidal beta and =0.58 ms, NVS=0.36
ms VS=0.80 ms for energy confinement time. At higher currents, where only RFX and
RFX-mod VS data are available, τE is twice for RFX-mod compared to RFX.
2c.2 Scaling laws To better understand the phenomena underlying confinement, we have studied the dependence of βp and τE on the main plasma parameters for RFX and RFX-mod VS.
Poloidal beta shows the clearest scaling: all the VS data of stationary discharges can be fitted
by a single parameter exponential fit βp ∝ (Ip/N)-0.74 (regression coefficient R=0.9). The RFX thick shell discharges are better described by a two parameter fit βp∝Ip-0.46(Ip/N)-0.50 (multiple regression coefficient R=0.7). The additional negative dependence on plasma current obtained
in RFX is similar to that obtained in T2 experiment and to the βp∝Ip-0.56(Ip/N)-0.56 predicted by 3-D resistive MHD simulations performed by the
DEBSP code [Brunsell00]. The result of RFX-
mod VS, where the addition of the Ip as
independent parameter is not necessary in order
to have a good scaling, shows that by lowering
edge error fields (and then by controlling the
plasma-wall interaction), it is possible to obtain
the same βp at higher plasma current for a given
I/N.
Energy confinement time shows a less clear
dependence on the main plasma parameters. In
the RFX-mod VS case a two parameter fit
provides a relatively good regression
τE∝Ip0.72(Ip/N)-0.23 (multiple R=0.68), while a much worse (multiple R=0.3) regression τE∝Ip0.40(Ip/N)-0.16 is obtained in RFX, showing that other hidden parameters affect RFX results. A better scaling law is obtained for the VS data by a three parameter fit, using Ip, Ip/N and b8-15, the sum of the amplitudes of the toroidal field modes with m=1 and n=-15÷-8. The least
square fit of τE is drawn in Fig. 2.25. The goodness-of-fit has been tested by applying it to RFX-
mod NVS data, for which b8-15 is about 2÷3 times higher than for VS ones. Figure 2.25 shows that RFX-mod NVS data are also relatively well described. The explicit dependence of τE on b proves the beneficial effect of the boundary control up to the core. The dependence on b is qualitatively in accordance with the Rechester-Rosenbluth (RR) theory of transport in a
stochastic magnetic field, though numerical results [D’Angelo96] based on that theory would
predict a power dependence of -1.5. It has to be noted that the best correlation was obtained
using m=1 modes with n≤-8 while the mode with the highest amplitude is typically n=-7
(usually the central one in RFX-mod). This is in agreement with previous observations that
showed a low effect on stochasticity of the innermost resonant mode.
0
0.5
1
1.5
0 0.5 1 1.5
RFX-mod VSRFX-mod NVS
τ E (m
s)
1.1 10-13 I 1.17 (I/N)-0.35 b8-15
-0.61 (A*Am*T)
Fig. 2.25: Three parameters fit of τE of VS discharges applied to both VS and NVS RFX-mod discharges.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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2c.3 Particle transport Interaction between the dynamo modes locks them in phase. The locked mode (LM) produces a
non axial-symmetric deformation of the last closed magnetic surface (LCMS) [Martini06]. The
deformation affects transport introducing non axial-symmetric effects locally modifying both
the density profile and the influx from the wall. Due to the plasma-wall interaction, density
profiles close to the locking position have a steeper edge gradient than at other toroidal
positions [Lorenzini06] and particle influx is
higher [Valisa01]. Controlling the edge radial
magnetic field by VS greatly reduces the
deformation amplitude, but the effect is still
present.
Figure 2.26 shows, as a function of the Ip/N
parameter, the peaking factor (P) defined as the
ratio of the central density to the average
density. In figure 2.26, to avoid LM effect, only
density profile measurements far from locking
position are considered. The data show that
there is no difference on density profiles
between RFX and RFX-mod. This is confirmed by
performing a multivariable regression of the
peaking factor, which gives the scaling
P∝Ip0.14N-0.27 (multiple R=0.7) for RFX-mod data
and a similar one (with a lower correlation) for
RFX.
The negative power dependence on density can be
explained in terms of neutral particle source that
becomes closer to the wall when density
increases. The small positive dependence on
plasma current is less obvious. It could result
from a lower plasma core transport due to a
reduced magnetic stochasticity at higher plasma
currents.
Although density profiles in RFX-mod VS and in
RFX are similar, particle transport is globally
reduced in RFX-mod, particularly at the highest
plasma currents where RFX was strongly affected
by LM. This results from the lower particle influx
of RFX-mod discharges. In RFX-mod particle influx measured at the Hα diagnostic section
shows no correlation with the toroidal position of the m=1 helical component of the LM
0
2
4
6
8
10
12
14
-150 -100 -50 0 50 100 150
Γ H (*
1021
m-2
s-1
)
φo-φHα (°)
(a)
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6
Γ H (*
1021
m-2
s-1 )
ne (*1019 m-3)
(b)
Fig. 2.27: Particle influx for RFX-mod (VS) discharges with plasma current >800 kA. a) Particle influx versus toroidal distance of the m=0 LCMS shrinking from Hα measurement; b) Particle influx versus average plasma density.
0
0,4
0,8
1,2
1,6
0 2 4 6 8 10 12
RFX-mod VSRFX
P=n e
(0)/<
n e>
Ip/N (Am)
Fig. 2.26: Density profile peaking for RFX and RFX-mod VS discharges.
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2006 Activity Report Technical Scientific Committee 18 January 2007
- 24 -
deformation. In discharges with plasma current higher than 800 kA a small increase of particle
influx is present when the toroidal position of the m=0 shrink component of LM deformation is
very close to the Hα measurement section (Fig. 2.27a). On average the influx linearly depends
on the density (Fig. 2.27b) with a value of 3⋅1021 m-2s-1 for a density of 2.5⋅1019 m-3, which
corresponds to a global particle confinement time of about 2 ms. In the same plasma current
range (>800 kA) on RFX about 40% of particle influx came from a region close to the m=1 LM.
Due to the strong wall interaction and the poor particle confinement, in RFX the global influx
was independent of density, with a value ≥6⋅1021 m-2s-1 more than twice than in RFX-mod VS.
Particle transport is simulated using a 1-D transport code that solves the transport equation.
Following the RR theory of diffusion in a stochastic magnetic field, we include in the convective
velocity component of particle flux a velocity proportional to the stochastic coefficient (Dst) and
the normalised temperature gradient:
Vst = -Dst(r)2T(r,t)
∂T(r,t)∂r
To find Dst we parameterise it with five free parameters in the following way:
Dst(r) =(D0- De1)(1-rα)β + De2r30+ De1
The profile of atoms coming from the wall is computed with the Monte Carlo code NENE
(NEutrals and NEutrals). The interaction of the particles with the wall is modelled using the
results of the TRIM code (TRansport of Ion in the Mass), a Monte Carlo code for simulation of
sputtering, ion reflection and ion implantation in structure-less solids.
We evaluate the Dst on RFX and RFX-mod by
simulating the same typical density profile at
=3⋅1019 m-3. For RFX-mod the influx is
ΓH=3⋅1021 m-2s-1 and the exponent of
temperature profile is αT=3; for RFX we use
ΓH=6⋅1021 m-2s-1 and αT=4 because flatter
temperature profiles were found in RFX.
Figure 2.28 shows the diffusion coefficient
and the consequent outward velocity in the
two cases. As it can be expected from halving
the particle influx, the diffusion coefficient of
RFX-mod is approximately halved on the
whole plasma cross-section. Although the
errors in Dst are large, the result seems to
indicate that in RFX-mod the particle
confinement improves on the whole cross-
section as an effect of a simultaneous
reduction of the plasma-wall interaction and
of the core magnetic stochasticity.
0
10
20
30
40
50
60
RFXRFX-mod VS
Dst
(m2 s
-1)
(a)
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1
v st (
ms-
1 )
r/a
(b)
Fig. 2.28: Diffusion coefficient and stochastic velocity obtained for RFX (red solid curves) and RFX-mod VS (black dashed curves).
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2006 Activity Report Technical Scientific Committee 18 January 2007
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2c.4 Energy transport The introduction of the active control system in
RFX-mod strongly influences plasma thermal
properties. They have been investigated
through the measurements provided by the
main Thomson scattering (TS) diagnostic that
has routinely operated since the beginning of
RFX-mod experimental campaigns [Alfier06a,
Paccagnella06]. In particular, the longer
discharges obtained with the VS, (from ~100ms
to ~300ms), allow to fully exploit the burst of
10 laser pulses of the TS diagnostic, so
increasing the available statistics.
Energy transport is greatly improved in RFX-
mod VS operations. The maximum of the central
electron temperature, Teo, increases nearly
linearly with plasma current up to 1 MA while
RFX showed electron temperature saturation
over 800 kA (see Fig. 2.29), giving a Teo in RFX-
mod VS about 30% higher than in RFX
discharges.
Another consequence of the active control is the
change in the temperature gradients: edge and
core local gradients, ∇Tedge and ∇Tcore, are
obtained by a linear fit of measured points in |r/a|>0.7 and |r/a|~0.5 respectively. ∇Tedge gets
steeper with active control (see fig.2.30). As far as ∇Tcore is concerned, the high spatial
resolution allows also to appreciate a systematic change, with a slight steepening of the core
gradient with the virtual shell passing from an average value of ~0.4 eV/mm in NVS to 0.6
eV/mm in VS.
Higher core electron temperature and steeper edge gradients indicate a decrease of electron
heat transport in RFX-mod VS. An estimate of such a reduction is obtained by applying the 1D
steady state power balance equation [Pasqualotto99]. The effective thermal conductivity, χeff
(Fig. 2.31), is deduced by using the single fluid equation:
χeff = -q⊥(r)/[ne(r)·∇Te(r)]
in which the energy flux, q⊥(r), is evaluated by integrating the expression
∇q⊥(r) = Ω(r) - ε(r)
where Ω(r) = E(r)·j(r) is the ohmic power deposition profile and ε(r) is the experimental total radiation emissivity, mostly localized in the plasma edge and typically ranging from 5% to 20%
Fig. 2.30: ∇Te,ext vs Te(0), at I/N~[3e-14 – 5e-14 ] Am for Ip
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2006 Activity Report Technical Scientific Committee 18 January 2007
- 26 -
of the input power. The current density j(r) profile is reconstructed from external magnetic measurements with the µ&p-model. E(r) is calculated through a local Ohm’s law with Spitzer resistivity, with an effective charge assumed uniform over the line integral of a line-free visible
continuous emission.
Edge radial field control during VS operation (blue profiles in Fig. 2.31) decreases the field
stochasticity in the core, with the effect of slightly reducing the minimum value of χeff by about
20%. Interestingly, the main effect is in the inner region, r/a~[0.5-0.7], where the temperature
gradient is still appreciably non-zero, and the average χeff is about 5 times lower than in the
NVS operation. Even better performances are obtained in the third case (green profiles in Fig.
2.31): it is characterised by low amplitude of all modes at the edge and relatively large
amplitude of the internal n=-7 mode thus realising a QSH state. This causes an increased
electron temperature and the formation of a significant temperature gradient in the core
region, shown in Fig. 2.31. The presence of the helical structure is confirmed by SXR
tomography.
2c.5 High density limit Among the operational limits of magnetically confined fusion plasmas the upper density limit,
peculiar to all major magnetic configurations (Tokamaks, Stellarators, Reversed Field Pinches)
[Greenwald02], is of great importance for its direct impact on fusion performance, which
depends on ne2 f(T), with f(T) a function of the plasma temperature. It has been previously
demonstrated that RFX-mod features an upper density limit remarkably well defined by the
Greenwald’s law found in Tokamaks despite the many differences between the two magnetic
configurations [Valisa04].
The density limit in RFX-mod has been analysed both in its experimental evidences and in
terms of the related edge transport properties in the spirit of a continuous comparison with the
findings in the other magnetic configurations [Valisa06]. In particular, discharges have been
Fig. 2.31: χeff and corresponding Te profiles in three representative profiles, in NVS (brown), VS (blue) and an optimum case (green).
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2006 Activity Report Technical Scientific Committee 18 January 2007
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produced near the limit with the aim of analyzing the behaviour of the radiated power, of the
edge plasma parameters and of the edge turbulence, while the trajectory of the plasma
discharge in the high density region has been modeled by means of the 1-D transport code
RITM [Telesca04].
We have found that for RFX-mod the database does not contain discharges with densities close
to the limit and, at the same time, with sustained plasma current, which instead is always
decaying at very high density. According to edge measurements, particle diffusion in the last
few cm of the plasma does not increase in conditions close to the density limit, while the edge
electron temperature does not decrease below 10 eV. The simulations made by RITM show
instead that the mechanism producing the density pump out observed in the experiment is
compatible with a generalized increase of the transport parameters that change mainly in the
core and in the periphery region but not significantly at the very edge. On the other hand, in
RFX-mod the density limit is not a truly
radiation limit in the sense that 100% of the
power input is never radiated: the radiated
power fraction, including the contribution of
the region of the locked modes, reaches
relatively low values, around 30-40 %, at the
highest densities. The origin of the current
decay at values of the density well below the
limit remains to be clarified, but the radiation
pattern in the region of the locked modes seems
a good candidate.
Indeed the width of the radiating layer shown
in Fig. 2.32, poloidally symmetric and
toroidally asymmetric where the plasma
interacts with the wall, appears to erode energy
from the plasma core well inside the reversal
surface and could well be the reason for plasma
cooling, increased resistivity and subsequent current decay, which in the RFP is guaranteed to
be soft by the intimate link between current and toroidal flux. This picture resembles the
MARFE of a Tokamak , with opposite geometry because of the opposite weight of toroidal and
poloidal fields at the edge.
2c.6 Plasma Flow in RFX-mod In RFX-mod, 4 arrays of 10 lines of sight have been recently intalled for performing
spectroscopic measurements of the plasma impurity rotation. During 2006 campaigns the new
systems have been extensively used for collecting data. We focussed particularly on the
Fig. 2.32: (a) reconstruction of the radiated power per unit of toroidal length vs the toroidal angle. The bolometer section is at 00. (b) Tomography of the radiation pattern when, during its toroidal motion, the maximum of the emission crosses the bolometer position at 00. (c) Tomography of the radiated power outside the strong emission peak.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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comparison between operations
with and without Virtual Shell
(VS), and on the separate role of
m=0 and m=1 magnetic
perturbations on carbon flow
pattern.
Regarding the first topic, we
observed that while the scaling of
the C V toroidal flow maintains in
both cases the decreasing
dependence on the electron density,
in operations with VS we registered
a clear reduction of the toroidal
rotation velocities (see Fig. 2.33).
C II flow is better suited for
following the behavior of edge flow
pattern in the presence of an external magnetic perturbation. In 2006 we singled out that the
change in the C II toroidal flow direction is related to the presence of the m=0 magnetic
perturbation and its typical deformation of the plasma shape.
2d Edge phenomena
2d.1 Edge turbulence analysis with the Gas Puff Imaging diagnostic. The Gas Puff Imaging diagnostic [Agostini06,
Cavazzana04] is widely used in the RFX-mod
experiment to study the edge turbulence,
measuring the propagation velocity of the edge
fluctuations and characterizing the coherent
structures that are considered the main cause of
anomalous particle transport in the fusion
plasmas. The characterization of the turbulence
was carried out for different plasma conditions,
studying the link between edge fluctuations and
the main plasma density. In Fig. 2.34 the scaling
of the toroidal velocity of the fluctuations as a
function of the plasma density normalized to the Greenwald one is shown. Each black point is
an average over 10 ms during the flat top phase of the discharges; the clear dependence of the
toroidal velocity on the density displays a saturation at about –20 km/s at n/nG >0.35
[Scarin06].
n/nG
vΦ (km/s)
Fig. 2.34: Scaling of the toroidal velocity of the edge fluctuations as function of the density normalized to the Greenwald one. The black dots are the experimental points, the red ones show the average trend.
with VS
w/o VS
Fig. 2.33: C V toroidal flow velocity with and without Virtual Shell operations along line of sights with different impact parameter (colored lines). The figure shows a reduction up to 5 km/s in the inner chords when VS has been operated.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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As particle transport at the edge depends on the presence of the coherent structures, the same
scaling with the n/nG parameter was studied for the density of these coherent vortices. Two
methods are applied for counting them. One is based on the continuous wavelet transform and
the Local Intermittency Measurement (LIM)
[Antoni01]; the second method [Sattin06]
assumes that the PDF of the GPI signals can be
fitted by two Gamma functions, one is due to the
uncorrelated fluctuations and the other to the
coherent part. In Fig.2.35 the scaling of the
linear density of bursts measured with the LIM
method, and the coherent fraction of the signal
extracted with the two Gamma functions fit of
the PDF are shown as a function of plasma
density. The two scalings are in agreement: the
edge vortices increase their contribution to the
signals as the parameter n/nG increases. At high density, the turbulence seems to saturate as
shown for the toroidal velocity of fluctuations.
The GPI diagnostic can also provide a 2D imaging of the edge structures with high time
(100 ns) and spatial (5 mm) resolution for the whole discharge duration; as the diagnostic
measures the line integrated emission, a tomographic algorithm is developed. Actually with the
GPI the 2 dimensional evolution
and motion of the edge structures
can be studied. An example of an
inverted pattern is shown in
Fig.2.36.
Due to the unfavorable curvature
of the magnetic lines, fast CCD
cameras (widely used in
tokamaks) cannot be used in the
RFP devices, and the GPI is a
good alternative to them for the
studies of the edge blob.
2d.2 Edge magnetic fluctuation analysis The full set of Integrated System of Internal Sensors (ISIS, [Serianni04]) of magnetic probes
has been put into operation during 2006 and used to obtain a characterization of the high
frequency fluctuations of the three components of the magnetic field (Br, BP, BT). The probes
are located behind the graphite tiles, which form the first wall of the machine, and consist of
pick-up coils measuring the time derivative of the magnetic field. The BT probes are placed in
Fig. 2.35: Scaling of the coherent vortices number as function of plasma density. Red circles: linear density of burst counted with the LIM method; blue squares: fraction of coherent part of the fluctuation measured with the 2 Gamma function
Fig. 2.36: Reconstructed emission profile for one RFX-mod shot. Left: reconstruction with back-projection algorithm; right: inversion with the tomographic algorithm. The vertical black line is the radial position of the vacuum vessel.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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one poloidal array in 8 equally spaced positions and in two toroidal arrays, each consisting of
48 equally spaced coils and covering the full toroidal circumference, in two opposite poloidal
positions (top-bottom). The sampling frequency for the BT probes is up to 2 MHz, while the
estimated bandwidth of the measurement is up to 300-400 kHz. An experimental analysis of
the magnetic BT fluctuation levels in different frequency ranges has been performed in a wide
range of experimental conditions.
Various regimes of plasma current density IΦ, I/N
parameter and reversal parameter F have been
explored, along with the dependence of the
fluctuation levels on the Lundquist number S,
which is the ratio of the resistive diffusion time to
the Alfvén time [Zuin06]. Particular attention has
been dedicated to the dynamic behavior of F, as this
is observed in RFX-mod to exhibit large
fluctuations, related to relaxations of the magnetic
field profile during the discrete Dynamo Relaxation
Events (DRE). Moreover, an investigation of the
effect of the Virtual Shell has been performed.
An increase of the magnetic activity related to even
m modes is observed for the low frequency part of
the spectrum when moving from shallow towards
deeper reversal, when the continuous dynamo
action is taken into account. During the discrete
relaxation events, when deeper F values are
dynamically reached, a strong activity with odd m
at high frequency is observed (Fig. 2.37). A
reduction of fluctuation level has been observed to
be induced by the Virtual Shell, with a strong
asymmetrical behavior in the toroidal direction. In particular, the most significant reduction
was observed on the signals taken at the position of the locked mode (Φlock), while the weakest
reduction was measured at Φ>Φlock. It is important to say that the effect is mostly visible in the
low frequency component of the fluctuation, while at frequency above 60 kHz the magnetic
signals seem almost unaffected.
In Fig. 2.38 the power spectra of BT signals obtained in all the toroidal positions are shown in a
color-scale plot. A non axi-symmetric behavior around the locked mode position is observed to
persist despite the action of the VS.
Fig. 2.37: RMS of BT signals from the ISIS system vs F: a) f
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In a large set of discharges with active Virtual Shell, an increase of the magnetic fluctuation
with I/N at all the explored time scales has been observed. A robust high frequency activity
with odd m number develops during the discrete magnetic relaxation events. It is found a
scaling of the fluctuation levels with S, comparable with the theoretical numerical prediction
[Cappello96], when the low frequency part of the
spectrum is analyzed, while the magnetic
fluctuations at higher frequency do not show any
clear dependence on S.
By applying the Fourier transform to the signals
from the toroidal arrays, the fast dynamics of the
MHD (tearing) modes can be determined. In
particular, it has been observed that the
development of DREs corresponds to the rapid
formation of a strongly localized magnetic
perturbation at the position of the locked mode.
This perturbation, characterized by a main m=0
periodicity, is then observed to move toroidally,
both clockwise and counter-clockwise, with two
different velocities, as can be seen in Fig. 2.39.
2d.3 Edge Turbulence measurements by probes Similar features have been observed in the edge turbulence of different devices and in
particular bursts on electrostatic fluctuations have been observed in the edge region of several
fusion experiments including tokamaks stellarators and reversed field pinches (RFP). In
different experiment a coherent part has been detected in the edge fluctuations and has been
associated to the presence in the edge region of coherent structures with eddy features or blobs
of density. It is believed that these structures play a major role in driving the transport in the
edge region. In particular in the RFP configuration it has been found that strong bursts,
although representing a small fraction of the signal, carry up to 50% of the particle flux losses.
Turbulence features in the edge region have been investigated by using the new and original
probe system, dubbed “U-probe”. The system is constituted by two blocks toroidally spaced by
about 90 mm, each of them equipped with a matrix 5 (toroidally) times 8 (radially) of Langmuir
pins and a radial array of seven 3-axial magnetic probes. The diagnostics peculiarity allowed a
detailed analysis of the fluctuations both on electrostatic and magnetic quantities with a radial
resolution of 6 mm, the high sampling rate (5 MHz) and the relative bandwidth allowed a high
time resolution as well. Concerning electrostatic parameters the probe provided simultaneously
local measurements of radial profiles of floating potential Vf, ion saturation current, Is, and
electron temperature Te. Furthermore in the same location the three components of magnetic
field fluctuations, Br, Bθ and Bt, have been measured. The probe has been inserted in different
Fig. 2.39: a) Toroidal contour plot of Bt signals from the ISIS system during a DRE (color scale is in Tesla units) b) time behavior of the reversal parameter F.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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radial position in order to investigate the edge region up to r/a~0.9, spanning a radial region of
36 mm at each shot. Due to probe insertion the plasma current has been limited to 300-350 kA
with an average plasma density of about 2 1019m-3.
By using the statistical techniques described in [Antoni01] the occurrence of intermittent burst
have been identified in the fluctuation time series. The spatial shape of electrostatic and
magnetic structures have been investigated in the cross field plane (r, phi) by applying a
conditional average technique on a time window including the intermittent events.
An example of this kind
of analysis is shown in
Fig 2.40 where the
positive burst on ion
saturation current, Is,
have been used as
trigger events. It can be
observed that also
radially extended
structures on toroidal
and radial magnetic
field fluctuations are
associated to the
electrostatic ones, with
comparable or larger
size [Spolaore06].
It has been found that a
comparable size
characterizes HeI
emission structures observed by a Gas Puff Imaging diagnostics resolved at 10 MHz
[Cavazzana04, Agostini06] and Is fluctuations structures measured by Langmuir probes. It is
worth noting that the velocity of the structure measured by the GPI system is consistent with
the average E×B velocity measured by the probes, and in particular the time lag between the
structures observed by the two diagnostics is consistent with the hypothesis of a density
structure traveling at the average E×B velocity between their two toroidal locations
[Spolaore06].
The U-Probe system has also been extensively used to investigate the shear flow generation
mechanism, and particularly the turbulence-induced plasma flows via Reynolds Stress
[Vianello05]. The simplest model implying this mechanism may be inferred from an ensemble
average of the momentum balance equation:
Fig.2.40: Conditional average with trigger on positive events detected on Is fluctuations at r=446.5 mm. From top to bottom panels: (Br(r,t)-< Br (r,t)>)/σ (left); (Br (t)-< Br (t)>)/σ at r=446.5 mm (right); analogous quantities for Bt and Is.
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2006 Activity Report Technical Scientific Committee 18 January 2007
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φφφφ
φφ νµρµρVVV
BBbbvvV r
rr
rrrt
2
00
~~~~ ∇+⎟⎟
⎠
⎞⎜⎜⎝
⎛−∂=
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡−∂+∂
where each field has been divided into its average and fluctuating part, and ν is the kinematic
viscosity. The term ⎥⎥
⎦
⎤
⎢⎢
⎣
⎡−=
0
~~~~
µρφ
φφ
bbvvR
rrr is the generalized Reynolds stress,
whereas its velocity and magnetic components are
referred also as Electrostatic Reynolds Stress (ERS) and Maxwell Stress (MS) respectively. Moving the probe on a shot to shot basis, the profiles
of the Reynolds and Maxwell stresses have been
measured for the first time in RFX-mod. In figure
2.41 these profiles are shown together with the E×B velocity profile obtained from floating potential and
temperature measurements. The velocity profile
exhibits a double shear layer. As already observed in
Extrap-T2R [Vianello05] also in RFX-mod it is fairly
evident that the coupling between perpendicular
velocities becomes important inside the plasma,
beyond the nominal positions of the graphite tiles,
where also a strong gradient occurs. Specifically we
are interested in the innermost shear region (r≤ 440
mm) where ERS exhibits a strong gradient whereas
MS is lower with an almost flat profile. The high
spatial and temporal resolution of the
experimental equipment allows also the estimate
of the temporal evolution of the various terms
entering the momentum balance equation. In
particular the temporal evolution of ERS and of
MS has been estimated through the Continuous
Wavelet Transform (CWT) technique [Vianello06].
In Fig. 2.42 a sample from a single shot of the time
traces of φV and of the radial derivates of ERS and
MS are shown. In particular in panel (b) the
comparison between φVt∂ and φvvrr ~~∂ shows the
clear correlation between plasma acceleration and
Fig. 2.41: (a) Drift velocity profiles (b) Total Reynolds stress (c) Reynolds and Maxwell stress profiles. The vertical