Control of Magnetic Chaos & Self-Organization John Sarff for MST Group CMSO General Meeting Madison, WI August 4-6, 2004.

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.