Basic plasma parameters are used as input, of which Zeff is PPCD...
1
INTRODUCTION Measurements of the Hard X-ray (HXR) flux have been combined with CQL3D modelling to infer diffusion coefficient, fast electron population and current density during PPCD plasmas. EXPERIMENTAL SETUP Hard X-rays (>10KeV) emitted by runaway electrons via bremmstrahlung are measured using solid state CdZnTe detectors. CdZnTe detectors: 10mm x 10mm x 2mm ~10-300KeV energy resolution 2ms pulse width - 500KHz time resolution transimpedance amplifier built in. The output pulses from the detectors are digitized directly rather than pulse height discrimination and counting. ADVANTAGES: Software can distinguish noise and pile up better than simple pulse height analysers. Data stored as discrete events at definite times, allowing the data to be binned for low energy resolution with high time resolution, or simultaneously low time resolution with high energy resolution. Simple to implement DISADVANTAGES: Prior to processing, a lot of data must be stored, limiting shot length. time(ms) 0.0 0.1 0.2 0.3 2ms X-ray events are seen as Gaussian pulses, produced by a shaping amplifier - the amplitude is proportional to the energy. A 6MHz digitizer records the pulses, as shown on the right. Each pulse is then individually fit using a Gaussian fitting function. A combination of the width (determined by the shaping time of the amplifier) and the chisq of the fit are used to determing whether pile up has occured. pileup: time=16.7715 -0.001 0.000 0.001 0.002 0.003 -0.01 0.00 0.01 0.02 0.03 0.04 0.05 The data can then be fit using a double Gaussian. In this way the effective bandwidth can be increased, the dead-time due to pileup can be reduced. Pileup is still reduced by adjusting the solid angle of the detector. X-ray events during PPCD for shot= 1010425099 12 14 16 18 0 100 200 time X-ray energy (keV) 0 20 40 60 80 photon energy (keV) 0.001 0.010 0.100 1.000 HXR flux (erg/cm2/s/ster/eV) 8 10 12 14 16 18 20 22 time (ms) 0.00 0.05 0.10 0.15 0.20 HXR flux (erg/cm2/s/ster) Spectrum evolution during PPCD/Standard Plasmas 20 40 60 80 energy (KeV) 10 -5 10 -4 10 -3 10 -2 energy (ergs/cm^2/sec/ster/eV) PPCD PPCD STANDARD STANDARD 10 15 20 25 time (ms) 20 40 60 80 Energy (KeV) HXR Energy flux during 400kA PPCD plasmas PPCD APPLIED 8-20ms 2.5ms D40keV Simple analysis of raw data gives estimates for E|| and diffusion coefficient. In the period before saturation, ramp up is at a rate of D40keV/2.5ms This implies an upper limit on the parallel electric field of ~0.35V/m The time of saturation gives an estimate for connection length in the core of ~100km This corresponds to a diffusion coefficient of ~1m 2 /s More sophisticated analysis can be done - using CQL3D. CQL3D is a Fokker-Planck code which evolves the electron and ion distribution functions in space and time. J, B, Te, Ti, (Z eff ) f e,i evolved in r, velocity space and time resistivity E ll modified until E ll /resistivity matches input J ll NO YES Modify E ll and recalculate FP evolution Calculate HXR flux and other output Variables: radial diffusion coefficient (and optionally Zeff) Measured quantities Input to FP solver Modify radial diffusion coefficient (Zeff) to match HXR output Given ambient plasma conditions (equilibrium, Te,i,Ip, density) CQL3D evolves the electron distribution function. Diffusion (and optionally Zeff) are adjustable parameters E|| is internally adjusted (based on the computed resistivity) to match the input J|| Diffusion and Zeff are adjusted to best fit the data. t e 0 200 400 600 800 n e 0 5.0•10 12 1.0•10 13 1.5•10 13 j || 0 1 2 3 z eff 0.0 0.1 0.2 0.3 0.4 0.5 0 1 2 3 4 5 MA/m 2 cm - 2 eV t i r (m) Broad range of basic plasma parameters are input to the code. Z eff is a difficult measurement on MST due to the low ne and high n0. Extensive work has resulted in a measurement of Z eff during PPCD which is surprisingly high However, these plasmas had no boronization (MST has carbon and aluminium first wall). Basic plasma parameters are used as input, of which Z eff is the most controversial PPCD flux at time of MSTFit 0 20 40 60 80 100 Photon Energy (KeV) 10 -5 10 -4 10 -3 energy (ergs/cm 2 /sec/sr/eV) ../sxr_diff5_z4.5.dat ../sxr_diff5_z2.dat With Diffusion coefficient of 5m 2 /s, measured Z eff matches data well, even with Diffusion=0m 2 /s, Z eff ~3 needed Higher diffusion coefficients require a higher Z eff profile Given these input profiles, a good match to the measured HXR flux is found for a diffusion coefficient of ~5m2/s The resistivity drops due to the presence of runaway electrons Resistivity drop due to current carried by Runaway Electrons during PPCD 0.0 0.1 0.2 0.3 0.4 0.5 0.0 0.5 1.0 1.5 2.0 2.5 RA not included (same PPCD equilibrium, but Ell reduced to below Dricer field. RA included (PPCD) Resistivity/Spitzer Resistivity r (m) By reducing the parallel electric field to be less than the Dricer electric field, the runaway population can be reduced. There is a 25% increase in resistivity in the core (~same as the measured current peaking of PPCD plasmas over standard plasmas. Electron energy Current density No runaways With runaways 20 40 60 80 100 10 -2 10 -4 10 -6 10 -7 10 -5 10 -3 d 2 E/dtdk (ergs/cm 2 /sec/ster/eV) Photon Energy (KeV) Flux rate of data during PPCD 6 orders of Magnitude HXR Flux with Diffusion coefficient proportional to v th Is the diffusion dominated by magnetic stochasticity or electrostatic effects? The simulations shown earlier were with a constant diffusion coefficient - predicted HXR flux cannot be reconciled with measured data if one attempts the same simulation with a diffusion coefficient proportional to vth. The same plasma profiles were used, but the diffusion coefficient was assumed to follow a Rechester- Rosenbluth dependency, i.e. to be dominated by flow along stochastic magnetic field lines. This suggests that core transport during PPCD plasmas is dominated by electrostatic effects. Ongoing and future work: The hardware is being expanded to use 16 chords. This will allow radial resolution of the diffusion coefficient. A VME computer with 16 10Mhz, 12bit ADCs has been assembled. Data is recorded, then processed using IDL. The question of the effects of RF heating on the fast electrons will be addressed. Simulations have been performed using CQL3D. During EBW application, a large increase in the edge HXR flux is expected. Line integrated flux from 10-100KeV -1.0 -0.5 0.0 0.5 1.0 Impact radius 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Energy Flux (ergs/cm^2/sec/ster) 150kW 0,50kW Simulations of EBW into PPCD plasmas show an order of magnitude increase in flux in the edge Conclusions Measurement and analysis of HXR flux shows a clear confinement increase during PPCD plasmas over standard plasmas. Approximately 4 order of magnitude increase in flux seen Corresponds to a diffusion coefficient of ~5m 2 /s, and connection lengths of ~100km. Implies transport in the core may be dominated by electrostatic effects, not flow along stochastic field lines. 1-2% runaway electron population carries ~25% of current in the core, with a corresponding drop in the resistivity. Simulated parallel electric field matches measured value and confinement estimates. Measured HXR flux supports high Z eff measurements in core during PPCD plasmas. The array will help constrain the Diffusion coefficient as a function of radius. The arrays will also allow measurement of the EBW absorbtion and radial diffusion of heated electrons. Newly installed array on MST 0 n=1-15, m=0 + m=1 Current drive time (ms) 2 1 0 -1 E || (V/m) b f (G) 0 50 100 5 10 15 20 25 PPCD in MST During PPCD plasmas current is driven in the edge such as to drive the current normally generated by the dynamo. In doing so, the magnetic fluctuations are substantially reduced. High HXR's are only seen during the burst free periods. In cases where the magnetic fluctuations are not suppressed with same E|| programming - HXR's are not seen. Many thanks to Yves Peysson and Lena Delpech. Thanks to John Sarff for frequency doubling our VTR812's! This work was supported by U.S.D.O.E.
Transcript of Basic plasma parameters are used as input, of which Zeff is PPCD...
INTRODUCTIONMeasurements of the Hard X-ray (HXR) flux have been combined with CQL3D modelling to infer diffusion coefficient, fast electron population and current density during PPCD plasmas.
EXPERIMENTAL SETUPHard X-rays (>10KeV) emitted by runaway electrons via bremmstrahlung are measured using solid state CdZnTe detectors.
CdZnTe detectors:10mm x 10mm x 2mm~10-300KeV energy resolution2ms pulse width - 500KHz time resolutiontransimpedance amplifier built in.
The output pulses from the detectors are digitized directly rather than pulse height discrimination and counting.ADVANTAGES:Software can distinguish noise and pile up better than simple pulse height analysers.Data stored as discrete events at definite times, allowing the data to be binned for low energy resolution with high time resolution, or simultaneously low time resolution with high energy resolution.Simple to implementDISADVANTAGES:Prior to processing, a lot of data must be stored, limiting shot length.
time(ms)
0.0
0.1
0.2
0.3
2ms
X-ray events are seen as Gaussian pulses, produced by a shaping amplifier - the amplitude is proportional to the energy.
A 6MHz digitizer records the pulses, as shown on the right.
Each pulse is then individually fit using a Gaussian fitting function. A combination of the width (determined by the shaping time of the amplifier) and the chisq of the fit are used to determing whether pile up has occured.
pileup: time=16.7715
-0.001 0.000 0.001 0.002 0.003-0.01
0.00
0.01
0.02
0.03
0.04
0.05
The data can then be fit using a double Gaussian. In this way the effective bandwidth can be increased, the dead-time due to pileup can be reduced.
Pileup is still reduced by adjusting the solid angle of the detector.
X-ray events during PPCD for shot= 1010425099
12 14 16 180
100
200
time
X-ra
y en
ergy
(keV
)
0 20 40 60 80photon energy (keV)
0.001
0.010
0.100
1.000
HXR
flux
(erg
/cm
2/s/
ster
/eV)
8 10 12 14 16 18 20 22time (ms)
0.00
0.05
0.10
0.15
0.20
HXR
flux
(erg
/cm
2/s/
ster
)
Spectrum evolution during PPCD/Standard Plasmas
20 40 60 80energy (KeV)
10-5
10-4
10-3
10-2
ener
gy (e
rgs/
cm^2
/sec
/ste
r/eV) PPCDPPCD
STANDARDSTANDARD
10 15 20 25time (ms)
20
40
60
80
Ener
gy (K
eV)
HXR Energy flux during 400kA PPCD plasmasPPCD APPLIED 8-20ms
2.5ms
D40keV
Simple analysis of raw data gives estimates for E|| and diffusion coefficient.In the period before saturation, ramp up is at a rate of D40keV/2.5msThis implies an upper limit on the parallel electric field of ~0.35V/mThe time of saturation gives an estimate for connection length in the core of ~100kmThis corresponds to a diffusion coefficient of ~1m2/s
More sophisticated analysis can be done - using CQL3D.
CQL3D is a Fokker-Planck code which evolves the electron and ion distribution functions in space and time.
J, B, Te, Ti, (Zeff) fe,i evolved in r, velocity space
and time
resistivity
Ell modified untilEll/resistivity matches input Jll
NO
YES
Modify Ell andrecalculate FP
evolution
Calculate HXR flux and other output
Variables: radial diffusion coefficient (and optionally Zeff)
Measured quantitiesInput to FP solver
Modify radial diffusion coefficient (Zeff)to match HXR output
Given ambient plasma conditions (equilibrium, Te,i,Ip, density) CQL3D evolves the electron distribution function.
Diffusion (and optionally Zeff) are adjustable parameters
E|| is internally adjusted (based on the computed resistivity) to match the input J||
Diffusion and Zeff are adjusted to best fit the data.
te
0200
400
600800
ne
0
5.0•1012
1.0•10131.5•1013
j||
0
1
2
3
zeff
0.0 0.1 0.2 0.3 0.4 0.5012345
MA/
m2
cm-2
eV ti
r (m)
Broad range of basic plasma parameters are input to the code.
Zeff is a difficult measurement on MST due to the low ne and high n0.
Extensive work has resulted in a measurement of Zeff during PPCD which is surprisingly high
However, these plasmas had no boronization (MST has carbon and aluminium first wall).
Basic plasma parameters are used as input, of which Zeff is the most controversial
PPCD flux at time of MSTFit
0 20 40 60 80 100Photon Energy (KeV)
10-5
10-4
10-3
ener
gy (e
rgs/
cm2 /s
ec/s
r/eV)
../sxr_diff5_z4.5.dat
../sxr_diff5_z2.dat
With Diffusion coefficient of 5m2/s, measured Zeff matches data well, even with Diffusion=0m2/s, Zeff ~3 neededHigher diffusion coefficients require a higher Zeff profile
Given these input profiles, a good match to the measured HXR flux is found for a diffusion coefficient of ~5m2/s
The resistivity drops due to the presence of runaway electrons
Resistivity drop due to current carried byRunaway Electrons during PPCD
0.0 0.1 0.2 0.3 0.4 0.50.0
0.5
1.0
1.5
2.0
2.5
RA not included (same PPCDequilibrium, but Ell reducedto below Dricer field.
RA included (PPCD)
Res
istiv
ity/S
pitz
er R
esis
tivity
r (m)
By reducing the parallel electric field to be less than the Dricer electric field, the runaway population can be reduced. There is a 25% increase in resistivity in the core (~same as the measured current peaking of PPCD plasmas over standard plasmas.
Electron energy
Cur
rent
den
sity
No runawaysWith runaways
20 40 60 80 100
10-2
10-4
10-6
10-7
10-5
10-3
d2E/
dtdk
(erg
s/cm
2 /se
c/st
er/e
V)
Photon Energy (KeV)
Flux rate of data during PPCD
6 orders of Magnitude
HXR Flux with Diffusion coefficient proportional to vth
Is the diffusion dominated by magnetic stochasticity or electrostatic effects?
The simulations shown earlier were with a constant diffusion coefficient - predicted HXR flux cannot be reconciled with measured data if one attempts the same simulation with a diffusion coefficient proportional to vth.
The same plasma profiles were used, but the diffusion coefficient was assumed to follow a Rechester-Rosenbluth dependency, i.e. to be dominated by flow along stochastic magnetic field lines.
This suggests that core transport during PPCD plasmas is dominated by electrostatic effects.
Ongoing and future work:
The hardware is being expanded to use 16 chords. This will allow radial resolution of the diffusion coefficient.
A VME computer with 16 10Mhz, 12bit ADCs has been assembled. Data is recorded, then processed using IDL.
The question of the effects of RF heating on the fast electrons will be addressed. Simulations have been performed using CQL3D.
During EBW application, a large increase in the edge HXR flux is expected.
Line integrated flux from 10-100KeV
-1.0 -0.5 0.0 0.5 1.0Impact radius
10-6
10-5
10-4
10-3
10-2
10-1
100
Ener
gy F
lux
(erg
s/cm
^2/s
ec/s
ter)
150kW
0,50kW
Simulations of EBW into PPCD plasmas show an order of magnitude increase in flux in the edge
ConclusionsMeasurement and analysis of HXR flux shows a clear confinement increase during PPCD plasmas over standard plasmas.
Approximately 4 order of magnitude increase in flux seen
Corresponds to a diffusion coefficient of ~5m2/s, and connection lengths of ~100km.
Implies transport in the core may be dominated by electrostatic effects, not flow along stochastic field lines.
1-2% runaway electron population carries ~25% of current in the core, with a corresponding drop in the resistivity.
Simulated parallel electric field matches measured value and confinement estimates.
Measured HXR flux supports high Zeff measurements in core during PPCD plasmas.
The array will help constrain the Diffusion coefficient as a function of radius.
The arrays will also allow measurement of the EBW absorbtion and radial diffusion of heated electrons.
Newly installed array on MST
0
n=1-15,
m=0 + m=1
Current drive
time (ms)
210
-1E || (
V/m
)b f
(G)
050
100
5 10 15 20 25
PPCD in MSTDuring PPCD plasmas current is driven in the edge such as to drive the current normally generated by the dynamo. In doing so, the magnetic fluctuations are substantially reduced.
High HXR's are only seen during the burst free periods. In cases where the magnetic fluctuations are not suppressed with same E|| programming - HXR's are not seen.
Many thanks to Yves Peysson and Lena Delpech.Thanks to John Sarff for frequency doubling our VTR812's!
This work was supported by U.S.D.O.E.
