Statistical Properties of Broadband Magnetic Turbulence in the Reversed Field Pinch

Statistical Properties of Broadband Magnetic Turbulence in the Reversed Field Pinch

John Sarff

D. Craig, L. Frassinetti1, L. Marrelli1, P. Martin1, P. Piovesan1

1 Conzorzio RFX, Italy

CMSO Workshop on Magnetic Turbulence • Madison, WI • June 20-21, 2005

Spectral structure and intermittency in RFP turbulence.

10–4

10–8

10–12

P( n )(T2)

1 10 100Toroidal Mode, n

~ n–3/2

~ n–5/3

Standard

Reduced-Tearing

Standard

ReducedTearing

Marrelli et al., PoP 12, 2005

Outline.

• RFP basics and controllable conditions:

– Standard RFP (strong relaxation)

– Reduced-tearing RFP (weaker relaxation)

• Spectral structure: nonlinear cascade origin for high-k turbulence?

• Intermittency revealed in non-Gaussian and non-self similar statistics

Reversed Field Pinch (RFP).

• Toroidal, current-carrying

• Density, n ~ 1013 cm–3

• Temperature, Te,i ~ 1 keV

• B / B ~ 2% (B ≤ 0.5 T)~

MST

“Standard” RFP is self-organized, with a strong dynamo.

• Pronounced “sawtooth” events

strong dynamo

0 0.2 0.4 0.6 0.8 1r/a

2.0

1.5

1.0

0.5

0

–0.5

V/m

E||

neoJ||

10 20 30 40Time (ms)

–10

0

10

(G)

0

600

(G)Toroidal Flux

B~

MHD tearing instability produces largest fluctuations.

Tearing resonance:

€

q(r) =rBφ

RBθ

=mn€

0 = k ⋅B =mr

Bθ +nR

Bφ

01020301%0

Toroidal Mode, n

€

˜ B φ (a)

B

inner-mostresonant modem = 1, n = 6

Origin of fluctuations at high frequency, short wavelengths is not understood.

1 10 100 1000

Frequency (kHz)

10–4

10–8

10–12

P( f )(T2/Hz)

Frequency Power Spectrum

tearing(plasma rotation)

“Reduced tearing” RFP is more stable (and less reliant on magnetic self organization).

• Controlled inductive current drive.

0 0.2 0.4 0.6 0.8 1r/a

2.0

1.5

1.0

0.5

0

–0.5

V/m E|| neoJ||

0102030nBφ (a) / B~(%)1.51.00.50StandardPPCD1021027066,052

Toroidal Mode, n

Reduced Tearing

weak dynamo

Simultaneous reduction at all frequencies suggests high-k origin is connected to low-k tearing.

1 10 100 1000

Frequency (kHz)

10–4

10–8

10–12

P( f )(T2/Hz)

Standard

Reduced Tearing

Frequency Power Spectrum

Puzzling structure in the high-n toroidal mode spectrum.

10–4

10–8

10–12

P( n )(T2)

1 10 100

Toroidal Mode, n

~ n–3/2

~ n–5/3 Inertial cascade?

2-pt spectrum:

€

k x (ω) =φ(ω)

x2 − x1€

φ=tan−1[ ˜ B (x1), ˜ B (x2 )]

Wavenumber Power Spectra

Puzzling structure in the high-n toroidal mode spectrum.

10–4

10–8

10–12

1 10 100 0 100 300200

log semi-log~ n–3/2

~ n–5/3

€

k⊥ρ i ≈ 1

≈ exponential

Toroidal Mode, n Toroidal Mode, n

Wavenumber Power SpectraWavenumber Power Spectra

P( n )(T2)

Puzzling structure in the high-n toroidal mode spectrum.

10–4

10–8

10–12

1 10 100 0 100 300200

log semi-log~ n–3/2

~ n–5/3

€

k⊥ρ i ≈ 1

≈ exponential

Toroidal Mode, n Toroidal Mode, n

Wavenumber Power SpectraWavenumber Power Spectra

P( n )(T2)

Two possibilities:

(1) Narrow inertial band, n ~ 10-70 (but note “excess” power n >100)

(2) Dissipation scale, n ≥ 30 (but note R /i ~ 150)

Left and right propagating waves separated in 2-pt analysis.

Issues: – radial correlation length – sheared rotation

10–4

10–8

10–12

P( n )(T2)

0 300Toroidal Mode, n

–300

ion diamagneticdrift direction

1 10 100

Toroidal Mode, n

10–4

10–8

10–12

P( n )(T2)

Spectral structurenot “left-right” symmetric.

Turbulence exhibits temporal intermittency, partly associated with sawtooth cycle.

10 20 30 400

Time (ms)

dBdt

ReducedTearingPeriod

StandardPeriod

PDF of signal differences reveals non-Gaussian turbulence in standard RFP.

Standard

€

Sτ (t) = ˙ b φ (t) − ˙ b φ (t + τ )

Signal differences:

Probability Distributions

PDF of signal differences reveals non-Gaussian turbulence in standard RFP.

Standard

ReducedTearing

€

Sτ (t) = ˙ b φ (t) − ˙ b φ (t + τ )

Signal differences:

In contrast, turbulence inreduced-tearing RFPmore nearly Gaussian

Probability Distributions

Turbulence in not self-similar at different time scales.

€

P(Sτ )∝ e−b|Sτ |α

PDFs fit to stretched exponentials,characterized by shape parameter .

Standard

But in the reduced tearing RFP, it is nearly self-similar.

Standard

Reduced Tearing

Analogous behavior observed in the electrostatic particle transport of standard RFP.

V. Antonni et al., PRL 87, 045001 (2001)

€

Γes = ⟨˜ n ̃ v r ⟩~ ⟨˜ n ˜ E ⟩

Particle flux is intermittent, correlatedwith flux-regeneration events.

RFX reversed field pinch

Summary.

• Origin of high frequency, short wavelength magnetic turbulence appears

connected to dominant MHD tearing instability.

• Spectral structure indicates two possibilites:

1) Narrow inertial range, probably requiring independent source at high-k

2) Dissipation scale near to unstable tearing

enhancement of anomalous ion heating power density? (via

cascade)

• Plasmas with large tearing exhibit non-Gaussian, non-self-similar turbulence.

– Effects diminished when tearing is reduced.

– Similar to electrostatic turbulence