Particle Energization and the Tearing-Driven Turbulent Cascade · Bringing Space Down to Earth •...
Transcript of Particle Energization and the Tearing-Driven Turbulent Cascade · Bringing Space Down to Earth •...
Particle Energization and the Tearing-Driven Turbulent Cascade
John Sarff
A. Almagri, J. Anderson, A. DuBois, D. Craig*, D. Den Hartog, C. Forest, K. McCollam, M. Nornberg, P. Terry, D. Thuecks
and the MST Team(*Wheaton College)
Bringing Space Down to Earth • UCLA • Apr 10-12, 2017
The tearing-driven turbulent cascade and dissipation
• Connected challenges:– Multi-scale modeling framework that spans global instability to turbulent
dissipation– Diagnostics and methods that isolate and distinguish particle energization
processes
103 104 105 10610−6
10−5
10−4
10−3
10−2
10−1
100
101
Frequency (Hz)
Powe
r [J/(
m3 Hz)
]
Magnetic=B2/2μ0Kinetic=(1/2)mi ni V
2E× B
0
~
~
~
fci
The tearing-driven turbulent cascade and dissipation
103 104 105 10610−6
10−5
10−4
10−3
10−2
10−1
100
101
Frequency (Hz)
Powe
r [J/(
m3 Hz)
]
Magnetic=B2/2μ0Kinetic=(1/2)mi ni V
2E× B
0
~
~
~
fci
DrivingGradients
The tearing-driven turbulent cascade and dissipation
103 104 105 10610−6
10−5
10−4
10−3
10−2
10−1
100
101
Frequency (Hz)
Powe
r [J/(
m3 Hz)
]
Magnetic=B2/2μ0Kinetic=(1/2)mi ni V
2E× B
0
~
~
~
fci
DrivingGradients
Self-OrganizingFeedback
The tearing-driven turbulent cascade and dissipation
103 104 105 10610−6
10−5
10−4
10−3
10−2
10−1
100
101
Frequency (Hz)
Powe
r [J/(
m3 Hz)
]
Magnetic=B2/2μ0Kinetic=(1/2)mi ni V
2E× B
0
~
~
~
fci
DrivingGradients
Self-OrganizingFeedback
?
Dissipation:- mechanism(s)- scale(s)
-1.0 -0.5 0.0 0.5 1.0 1.50
200
400
600
800
1000
Tem
pera
ture
(eV
)
Time relative to reconnection (ms)
He2 +
D
H+
He2+
D
H+
MST reversed field pinch plasmas
• Magnetic induction is used to drive a large current in the plasma– Plasma current, Ip = 50-600 kA ; B < 0.5 T
– Inductive ohmic heating: 5-10 MW (input to electrons)– Ti ~ Te < 2 keV, despite weak i-e collisional coupling (n ~ 1019 m–3 )
– Minor radius, a = 50 cm ; ion gyroradius, ρi ≈ 1 cm ; c/ωpi ≈ 10 cmβ < 25% ; Lundquist number S = 5 ×104-6
q(r)
~ 0.2
minor radius, r0 a
conductin
g s
he
ll
m=1, n ≥ 6resonances
m=0,all n
1,61,7
1,8rBφRBθ
Minor Radius, r
Tearing instability drives a broadband turbulent cascade
Toroidicity allows distinct k|| = 0 resonant modes at many radii in the plasma:
0 = k ⋅B =mrBθ +
nRBφ
m = poloidal mode number
n = toroidal mode number
1 10 100 1000Frequency (kHz)
10–4
10–8
10–12
tearinginstability
ωci /2πρi ~ 1 cm
B2( f )(T2/Hz)
k ≥ 0.03 cm–1
Tearing instability drives a broadband turbulent cascade
Toroidicity allows distinct k|| = 0 resonant modes at many radii in the plasma:
0 = k ⋅B =mrBθ +
nRBφ
m = poloidal mode number
n = toroidal mode number
Linear Instability
Nonlinear Excitation
1 10 100 1000Frequency (kHz)
10–4
10–8
10–12
tearinginstability
ωci /2πρi ~ 1 cm
B2( f )(T2/Hz)
k ≥ 0.03 cm–1
The cascade is anisotropic and hints at a non-classical dissipation mechanism
• The k spectrum fits a dissipative cascade model (Y. Ren, PRL 2011; P. Terry, PoP 2009)
• Onset of exponential decay (dissipation) occurs at a smaller k than expected for classical dissipation
(T2-cm)
B2 (k)
(cm–1)
Wavenumber Power Spectrum
0 0.2 0.4 0.6 0.8 1.0 1.2
k
Tear
ing
Ran
ge
k||–5.4
10–4
10–6
10–8
10–10
10–12
10–14
New evidence for the onset of drift waves at intermediate scales
• Turbulence becomes kinetic energy dominant at • Signatures consistent with drift waves (Thuecks et al, PoP 2017)
103 104 105 10610−6
10−5
10−4
10−3
10−2
10−1
100
101
Frequency (Hz)
Pow
er [J
/(m3 H
z)]
Magnetic=B2/2μ0Kinetic=(1/2)mi ni V
2E× B
0
~
~
~
fci
104
105
106
−2 −1 0 1 2Fr
eque
ncy
(Hz)
k⊥ (cm−1)
2
4
6
8
10
k⊥ρs ≈ 0.2
Non-collisional Ion Energization
Powerful ion energization is associated with impulsive magnetic reconnection events
• Instantaneous heating rate up to 10 MeV/s (50 MW)
Time (ms)
(large-scale B)
Relative to Reconnection Event
Ti > Te
Heating is anisotropic and species dependent
• Ion distribution diagnostics on MST:– Rutherford scattering for majority ion temperature– Charge-exchange recombination spectroscopy (CHERS) for minority ions– Neutral particle energy analyzers
0.0
0.5
1.0
1.5
T (
keV
)
-2 -1 0 1 2
T
T||
C+6
Time (ms) Time (ms)
Heating is AnisotropicMinority Ions Hotter than Majority Ions
An energetic ion tail is generated and reinforced at each reconnection event
• Distribution is well-fit by a Maxwellian plus a power-law tail
BeforeEvent
AfterEvent
fD+(E) = A e –E/kT + B E–γ
Proposed Ion Heating Mechanisms
The models proposed for ion heating in the RFP are similar to those for the solar corona and wind
• Cyclotron-resonant heating:– Feeds off the turbulent cascade to gyro-scale– Preferential perpendicular heating, but with collisional relaxation– Preferential minority ion heating, since is larger where ωci is smaller– Mass scaling is predicted with dominant minority heating and collisional
relaxation
B2 (ωci )
Tangri et al., PoP 15 (2008)(similar to Cranmer et al)
Time (ms)
30 32 34 36 38 400
200
400( )
Tα
(eV
)
T||
[D]
T||
[C]
T⊥ [D]
T⊥ [C]
The models proposed for ion heating in the RFP are similar to those for the solar corona and wind
• Stochastic heating:– Feeds off large electric field fluctuations and a distinct chaotic diffusion
process– Monte Carlo modeling yields MST-like heating rates (Fiksel et al, PRL 2009)– Predicts mass scaling close to that observed
-0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6Time From Sawtooth (ms)
200
400
600
800
1000
(V/m
)
103 104 105 106 107
Frequency (Hz)
102
10-2
10-6
J/m
3 -H
z
B2 / 2μ0
12miniV
2E×B0
ErRMS
Does non-Alfvenic cascade help make heating more powerful?
Viscous heating is not sufficient
• No experimental evidence for the required large sheared flow• Perpendicular flow is dominant for tearing modes for which the classical viscosity
is small• Difficult to achieve the large impulsive heating rates seen in MST plasmas• See, e.g., Svidzinski et al, PoP 15 (2009)
The need for multi-scale modeling
• Fluid treatment of tearing instability and the self-organizing feedback is mature but does not encompass small scales– Nonlinear MHD and two-fluid models (NIMROD, DEBS)– Typical spatial resolution 0.3– Braginskii dissipation, sometimes artificially enhanced for numerical purposes
• A large-scale electric field (dynamo flux) is created in the self-organizing feedback– Energization on the largest scale, e.g., energetic ions– Two-fluid nature allows ions and electrons to respond differently
• Boundary conditions are important– Unavoidable consequence of being a confined plasma– Coupling to other modes like drift waves, even if they are stable– Boundary interfaces are generic, e.g., corona or magnetosphere
kρi
(Some) next step RFP experimental opportunities
• Diagnostics and methods that discriminate heating mechanisms– Limited measurements suggest ion heating is preferentially perpendicular– Test bed for wave-particle correlation study– Diagnostic challenge is significant, so understanding probably hinges on
modeling predictions for turbulence characteristics
• Plasma control improvements, e.g., current magnitude and duration– Lower the Lundquist number to isolate MHD regime (versus two-fluid)
– Increase access for both intrusive and nonintrusive diagnostics
• Inject plasmoids– Mix with tearing-driven turbulence– Increase beta– Form shocks
Computational model for tearing-relaxation recently extended to include two-fluid effects
• Nonlinear multi-mode evolution solved using NIMROD• Motivated by measurements that suggest coupled electron and ion relaxation
E = −V×B+ 1neJ×B− 1
ne∇pe +ηJ+
mene2
∂J∂t
nmidVdt
= J×B−∇p−∇⋅Πgyro −∇⋅νnmiW
Ohm’s law:
Momentum:
Relaxation process couples electron and ion momentum balance
Two-fluid relaxation signatures are measured, e.g., Hall emf
Hall emf
MHD emf
0.6 0.7 0.8 0.9 1.0−40
−20
0
20
40
0.6 0.7 0.8 0.9 1.0Normalized Radius
−40
−20
0
20
40
V/m
E||−η J||<j×b>/noe−<v×b>, Inferred
MHD emf (inferred)
Hall emf
NIMROD Computation Deep-Insertion Magnetic Probe in MST
The turbulent cascade is not as strong when nonlinear coupling at the driving scale is disabled
Frequency (kHz)
˜ B 2
during event with m=0
before event
during event w/o m=0
tearing
q(r)
~ 0.2
minor radius, r0 a
conductin
g s
he
ll
m=1, n ≥ 6resonances
m=0,all n
1,61,7
1,8rBφRBθ
Minor Radius, r
(1,6)
(1,7)
(1,8)
(1,9)
(0,1)
(0,1)
(0,1)
etc.
Schematic of 3-wave cascade:
m ≥ 2 branchdrives the cascadeto smallest scales
Same m = 0couples tomany m = 1
Ti (eV)
Toroidalflux
Mag energy(kJ)
TearingAmplitude
(G)
n=6 n=1 (m=0)
Particle energization correlates with power flow into the cascade
Time (ms)
New power supplies enable four orders of magnitude in Lundquist number, S ≈ 3 104-8
MHDCodes
New ProgrammablePower Supplies
Existing Power Supplies
Freq
uenc
y (k
Hz)
Time (ms)10 12 14 16 18 20 22
50
100
150
20
15
10
5
Dens
ity fl
uctu
atio
n Po
wer
(1038
m-4
/kHz
) 10-4
10-5
10-6
10-7
10-8
10-9
a)
b)
c)
R 0‹| n
e| 0.8›/ ‹n
e,0›
Δ
–
n e| (1019
m-4
)
Δ|
0.90
0.80
0.70
0.60
8
6
4
2
0
r/aGyrokinetic modeling for the tearing cascade is a next challenge
• GENE modeling identifies standard drift mode branches in RFP equilibria• Initially motivated by improved-confinement regime, but gradients in standard
conditions are close to marginal stability (if not unstable)
ne
∇ne
Linear
Nonlinear
Nonlinearw. b-tilde
Summary
• Ion heating and acceleration associated with magnetic reconnection from tearing instability is a powerful process in the RFP laboratory plasma– Gyro-resonant and stochastic processes are likely candidates to support the
observed rapid heating and other features– Energetic tail formation for ions and electrons
• Global self-organization strongly coupled to turbulence and dissipation– Correlations in electric and magnetic field fluctuations are a hallmark of
dynamo feedback– Inhomogeneity on the system scale, e.g., strong edge gradients– Global magnetic flux change drives produces ion runaway energization– Impact of transport processes, which can be quite different for ions and
electrons