Control of Magnetic Chaos & Self-OrganizationControl of Magnetic Chaos & Self-Organization
John Sarff
for MST Group
CMSO General Meeting • Madison, WI • August 4-6, 2004
Plasma control permits adjustment of magnetic reconnection and self-organization processes in the RFP.
r / a
Tor
oida
l,
r / a
Tor
oida
l,
Adjust Current Drive
Adjust Current Drive
Example: Reduce tearing fluctuations and magnetic chaos by current profile control.
Outline.
Control MHD tearing and consequent relaxation processes by:
• Adjustments to inductive current drive
– Reduce tearing by matching E(r) to more stable J(r)
– AC helicity injection (oscillating loop voltages)
• Adjustment of mean-field B(r) to include/exclude resonant surfaces
• Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH)
Other control techniques used previously:
– electrostatic probe biasing (edge current drive & rotation control)
– helical magnetic perturbations from external coils
Outline.
Control MHD tearing and consequent relaxation processes by:
• Adjustments to inductive current drive
– Reduce tearing by matching E(r) to more stable J(r)
– AC helicity injection (oscillating loop voltages)
• Adjustment of mean-field B(r) to include/exclude resonant surfaces
• Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH)
Other control techniques used previously:
– electrostatic probe biasing (edge current drive & rotation control)
– helical magnetic perturbations from external coils
Magnetic reconnection (resonant tearing) occurs at many radii in the RFP’s sheared magnetic field.
RFP Magnetic Geometry
Tearing resonance:
€
q(r ) =rBφ
RBθ
=mn
€
0 = k ⋅B =mr
Bθ +nR
Bφ
“Standard” induction produces a peaked current profile,
unstable to MHD tearing (free energy r J||/B ).
Standard RFP
–0.5
0.5
1.0
1.5
2.0
V/m
0
0 0.2 0.4 0.6 0.8 1.0ρ/a
E||
ηneo J ||(Zeff = 2)
Ohm’s law imbalance characteristicof steady induction in the RFP
€
E −ηJ ≠ 0
“Standard” induction produces a peaked current profile,
unstable to MHD tearing (free energy r J||/B ).
Standard RFP
–0.5
0.5
1.0
1.5
2.0
V/m
0
0 0.2 0.4 0.6 0.8 1.0ρ/a
E||
ηneo J ||(Zeff = 2)
Ohm’s law imbalance characteristicof steady induction in the RFP
€
E −ηJ ≠ 0
€
=−v × B + 1en J × B − 1
en∇pe + mee2n
∂J∂t
multiple dynamo-like effects possible(several observed)
Poloidal inductive current drive targeted to outer region reduces MHD tearing instability.
Measured E(r) Profiles
“Pulsed Poloidal Current Drive” (PPCD)
0102030Time (ms)1.00.50Bθ rms(%)1021027066~0–0.04–0.08Bφ( )a( )TStandardPPCD
0 0.2 0.4 0.6 0.8 1
ρ/a
–0.2
0
0.2
0.4
0.6
0.8
1.0
V/m Eφ
E||
Eθ@15 ms
Magnetic fluctuations reduced at all scales & frequencies.
0102030nBφ (a) / B~(%)1.51.00.50StandardPPCD1021027066,052
• Long wavelength amplitude spectrum
Frequency (kHz)
€
˜ B φ2 ( f )
(T2/Hz)
• Frequency power spectrum
PPCD
Standard
Toroidal Mode, n
Dynamo essentially absent with PPCD.
PPCDStandard RFP
Simple Ohm’s law satisfied
–0.5
0.5
1.0
1.5
2.0
V/m
0
0 0.2 0.4 0.6 0.8 1.0ρ/a
E||
ηneo J ||(Zeff = 2)
0 0.2 0.4 0.6 0.8 1.0ρ/a
0
0.5
1.0
1.5
2.0
/V m
E|| ηneo J ||
strong dynamo weak dynamo
(simple Ohm’s law satisfied)
Electron Te and energy confinement increase.
0.20.40.60.81.0Te1101001000χe(m2/ )s
Standard-PPCD Improved00.20.40.60.81 /r a( )KeV00.20.40.60.81 /r aStandard-PPCD Improved PPCD
PPCD
Stochastic magnetic diffusivity and heat transport reduced 30-fold in core.
€
χe
(m2/s)
r/a r/a
field line tracing
€
χR−R = vTe Dm
€
Dm = ⟨Δr2⟩/ΔL
€
χe = χ R−R
where magnetic chaos is strong (several
overlapping islands)
measuredmeasured
predicted “Rechester-Rosenbluth”
PPCDStandard
χR-R
χR-R
Anomalous ion heating probably reduced.
Ti(r) Profiles
• Standard: Pe-i < PCX and Ti / Te ~ 1 anomalous ion heating must occur
• PPCD: Pe-i ≥ PCX and Ti / Te ~ 0.5 collisional ion heating only??
PPCD
Anomalous ion heating probably reduced.
Ti(r) Profiles
• Standard: Pe-i < PCX and Ti / Te ~ 1 anomalous ion heating must occur
• PPCD: Pe-i ≥ PCX and Ti / Te ~ 0.5 collisional ion heating only??
Te StandardTe PPCD
PPCD
Outline.
Control MHD tearing and consequent relaxation processes by:
• Adjustments to inductive current drive
– Reduce tearing by matching E(r) to more stable J(r)
– AC helicity injection (oscillating loop voltages)
• Adjustment of mean-field B(r) to include/exclude resonant surfaces
• Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH)
Other control techniques used previously:
– electrostatic probe biasing (edge current drive & rotation control)
– helical magnetic perturbations from external coils
Nonlinear mode coupling appears important for anomalous momentum transport.
• Nonlinear torque:
€
R×⟨˜ J knl × ˜ B k⟩~ Ck, ′ k ,k− ′ k
′ k ∑ ⟨ ˜ B ′ k
˜ B k− ′ k ˜ B k sin(ϕ ′ k −ϕ k +ϕ k− ′ k )⟩
€
⟨ ˜ B 1 ˜ B 6 ˜ B 7sin(ϕ7 −ϕ6 −ϕ1)⟩ force on n=6
€
ϕ7 −ϕ6 −ϕ1
2520151050211050π/20–π/20n=1, m=0n=6, m=1n=7, m=1
(km / s)(G)(rad)
€
˜ B(n)
€
ω /kφ=6 n phase velocity–1.5–1.0–0.500.51.01.5 ( )Time from sawtooth crash ms
(plasma rotation)
Adjusting B(r) to exclude m = 0 resonance greatly reduces momentum loss & ion heating during relaxation events.
1,50,1~0.2m,nr/a10q(r)1,61,7
Shift q > 0 to remove m = 0 resonance
Adjusting B(r) to exclude m = 0 resonance greatly reduces momentum loss & ion heating during relaxation events.
1,50,1~0.2m,nr/a10q(r)1,61,7
n=1, m=0n=6, m=1n=7, m=1(km / s)(G)(G)˜ B ˜ B q(a).06.04.0240200402002005101520Time (ms)non-reversed
q(a) > 0n=6, m=1ω / kφ0 ( )q a = 0
No sudden rotation loss with small m = 0
Outline.
Control MHD tearing and consequent relaxation processes by:
• Adjustments to inductive current drive
– Reduce tearing by matching E(r) to more stable J(r)
– AC helicity injection (oscillating loop voltages)
• Adjustment of mean-field B(r) to include/exclude resonant surfaces
• Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH)
Other control techniques used previously:
– electrostatic probe biasing (edge current drive & rotation control)
– helical magnetic perturbations from external coils
Under come conditions, the tearing spectrum is dominated by one mode.
MST
RFXSoft x-ray image
Spontaneous “Quasi-Single Helicity” (QSH)
Magnetic & velocity fluctuations are single-mode dominated.
€
˜ B 1,n
€
˜ V θ1,n
(mT)
(km/s)
QSH Standard
QSH Standard
MHD dynamo is single-mode dominated in QSH.
€
⟨ ˜ v × ˜ B ⟩||,φ
(V/m)
QSH Standard
Outline.
Control MHD tearing and consequent relaxation processes by:
• Adjustments to inductive current drive
– Reduce tearing by matching E(r) to more stable J(r)
– AC helicity injection (oscillating loop voltages)
• Adjustment of mean-field B(r) to include/exclude resonant surfaces
• Tuning for empirically different resonant mode spectra, e.g., quasi-single-helicity (QSH)
Other control techniques used previously:
– electrostatic probe biasing (edge current drive & rotation control)
– helical magnetic perturbations from external coils
AC helicity injection using oscillating loop voltages.
€
Vφ = ˆ V φsinωt
€
Φ=ˆ V θω
sinωt + Φdc
apply oscillating V
€
∂K∂t
=2VφΦ−2 E ⋅BdV ∫ (K = A ⋅BdV)∫
€
⟨2VφΦ⟩=ˆ V φ ˆ V θ2ω
• Magnetic helicity balance evolution:
(Standard RFP: V , = constant)
AC helicity injection using oscillating loop voltages.
€
Vφ = ˆ V φsinωt
€
Φ=ˆ V θω
sinωt + Φdc
apply oscillating V
€
∂K∂t
=2VφΦ−2 E ⋅BdV ∫ (K = A ⋅BdV)∫
€
⟨2VφΦ⟩=ˆ V φ ˆ V θ2ω
• Magnetic helicity balance evolution:
(Standard RFP: V , = constant)
MHD behavior is altered when AC loop voltage applied.
Time (ms)
AC volts onrelaxation events entrained
€
Vθ
(V)
€
˜ B (G)
€
˜ B (G)
m = 0
m = 1
increasebetween
crash
Between-crash heating should help identify anomalous ion heating mechanism.
sawtooth crash
smaller heating atapplied frequency
Summary.
• Several methods to control and adjust MHD tearing-reconnection have been developed for the RFP.
• Characteristics and strength of consequent relaxation processes are adjustable.
• MST’s CMSO plans systematically include “PPCD”, “q > 0”, “OFCD”, etc. as tools to expose underlying physics.
Tearing occurs spontaneously, both from linear instability and nonlinear mode coupling.
€
∇r (J|| / B )
Core-resonant m=1 modes are largest, calculated to be linearly unstable from .
Edge-resonant m=0 modes grow from nonlinear coupling to the unstable m=1 modes.
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