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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
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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
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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
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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
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“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~
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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
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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)
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“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
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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
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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
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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)
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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)
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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.
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Turbulence exhibits temporal intermittency, partly associated with sawtooth cycle.
10 20 30 400
Time (ms)
dBdt
ReducedTearingPeriod
StandardPeriod
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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
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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
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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
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But in the reduced tearing RFP, it is nearly self-similar.
Standard
Reduced Tearing
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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
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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