Energetic-Particle-Driven Instabilities and Their Effects on Fast Ions

Energetic‐Particle‐Driven Instabilities and Their Effects on Fast Ions in a Reversed Field Pinch
Liang Lin1
in collaboration with J. K. Anderson2, D. L. Brower1, W. Capecchi2, W. X. Ding1, S. Eilerman2, C. B. Forest2, J. J. Koliner2, D. Liu3, M. D. Nornberg2, J. Reusch2, J. S. Sarff2
1University
of California Los Angeles, Los Angeles, CA 90095, USA
2University of Wisconsin–Madison, Madison, WI 53706, USA
3University of California, Irvine, Irvine, CA 92697, USA
55th Annual Meeting of the APS Division of Plasma Physics
Denver, Colorado
November 11‐15, 2013 Fast‐ion studies now emerging for the reversed field pinch.
• Fast ion confinement and transport can be quite different from that in tokamaks and other configurations:
‐ weak toroidal field => large fast‐ion β and strong drive
‐ large magnetic shear => increased stability
• 1 MW neutral beam injector on Madison Symmetric Torus (MST) provides a good test‐bed for fast ion studies in RFP.
• Provide opportunity to :
 connect with and contribute to tokamaks and other configurations
 validate important energetic‐particle physics
Main Observations  EP‐instabilities in a RFP exhibit: o dynamically‐evolving spatial structure o nonlinear three‐wave coupling o wave‐particle interactions
o enhanced fast‐ion transport  First direct measurement of internal magnetic fluctuations associated with EP‐instabilities by Faraday‐effect polarimetry
Outline • MST and Neutral Beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species ‐Dependence on q ‐Nonlinear interaction among multiple modes • Fast‐ion transport
RFP presents unique opportunity for energetic particle physics Reverse Field Pinch
Safety Factor Profile
q(r ) 
r B
1
R B
• Comparable Bθ and Bφ in a RFP lead to strongly sheared magnetic field and q<1.
1 MW neutral beam is tangentially injected along the direction of plasma current to maximize beam deposition.
MST
R=1.5 m
a=0.5 m Plasma Parameters
Ip ~ 300 kA
B0 ~ 0.3 T Te0 ~ 0.26 keV
ne0~ 1019 m‐3
Plasma equilibria remain toroidally axisymmetric with nested flux surface.
NBI Parameter
Specification
Beam Energy
25 keV
Beam Power
1 MW
Pulse Length
20 ms
Beam Fuel
H or D
Anderson et al., PoP 2013.
Classical TRANSP/NUBEAM modeling predicts centrally peaked fast ion density.
f  E , /  
f  R, Z 
R0=1.5 m
a =0.5 m Phase averaged Volume averaged • Fast ions are confined in the plasma core (r/a<0.4).
• Mainly passing particles with pitch v||/v=0.9.
Classical modeling predicts that core fast‐ion βf exceeds bulk plasma βbulk and core n f can reach 25% of ne.
Density profile
ne
Local profile

fast-ion  f
bulk plasma bulk
nf
Classical modeling predicts that core fast‐ion βf exceeds bulk plasma βbulk and core n f can reach 25% of ne.
Density profile
ne
Local profile

fast-ion  f
bulk plasma bulk
nf
• Core fast ion density is expected to be lower than classical prediction due to the onset of EP instabilities. Advanced polarimetry‐interferometry diagnostic is used to measure equilibrium and fluctuating quantities.
• Interferometry: 11 chords
∆R ~ 8 cm
 int   ne dz
ne 0 , ne
• Faraday‐Effect Polarimetry:  pol   ne Bz dz
Plasma
Schottky diode
time response ~ 1µs
J  , B , br , b , j
Advanced polarimetry‐interferometry diagnostic is used to measure equilibrium and fluctuating quantities.
• Interferometry: 11 chords
∆R ~ 8 cm
 int   ne dz
ne 0 , ne
• Faraday‐Effect Polarimetry:  pol   ne Bz dz
Plasma
• Magnetic Coils: b , b
Schottky diode
J  , B , br , b , j
m, n
• Tangential‐view Neutral Particle Analyzer:
charge exchange between circulating fast‐ions and background neutrals
time response ~ 1µs
Outline • MST and Neutral beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species ‐Dependence on q ‐Nonlinear interaction among multiple modes • Fast‐ion transport
Energetic‐particle‐driven modes are observed ~2.5 ms after neutral beam injection.
PNBI (MW)
Freq. (kHz)
Freq. (kHz)
Magnetic Spectrogram
200
0
140
n = 4 • NBI induced mode
m = 1, n=4
f plasma 
n = 5 • NBI induced mode
m = 1, n=5
0
1
• Global Tearing mode
24kV H‐beam into D‐plasma 0
16
18
20
Time (ms)
22
Ip = 300 kA
ne = 0.7x1019m‐3
24
Koliner et al., PRL 2012.
Single burst of the n=5 NBI‐driven mode
After band‐pass filter [60, 120] kHz ~
~
• Each burst has a duration 0.06 ms
( 160 Alfvèn times ) a / A
and a fishbone‐like structure.
• Ensemble analysis is performed over many bursts.
Measured frequency is significantly below predicted TAE frequency. Alfvèn Continuum • TAE gaps (n=4, 5) near 200‐300 kHz, located at mid‐radius.
‐STELLGAP (D. Spong)
• Observed Frequencies (Doppler‐shift corrected) are below TAE predictions.
Detected modes are not TAEs
Solid line: calculated freq. Dashed line : measured freq. in plasma frame Measured frequency is significantly below predicted TAE frequency. Alfvèn Continuum • TAE gaps (n=4, 5) near 200‐300 kHz, located at mid‐radius.
‐STELLGAP (D. Spong)
• Observed Frequencies (Doppler‐shift corrected) are below TAE predictions.
Detected modes are not TAE
fast‐ion density profile
• Continuum mode can be destabilized when drive overcomes damping. ‐ Energetic Particle Mode (EPM)
Density fluctuations associated with EP modes exhibit a spatial asymmetry, peaking in the core where fast ions reside. rms‐amplitude
 ne dz
ne
• Estimated level : [0.1, 0.1] ms
|  ne dz |max
~ 0.4%
 ne dz
R  Rmag  0.1 m
at .
 ne dz
phase
•  phase shift across the magnetic axis indicates an m=1 feature. Magnetic axis
Density fluctuations peak near , feature of continuum mode   k A
destabilized by strong drive.
Line‐integrated density fluctuations  ne dl
H‐beam into D‐plasma Frequency in plasma frame; Doppler shift removed.
Core magnetic perturbation associated with the dominant EP mode is measured by Faraday‐effect polarimetry.
[0.1, 0.1] ms
Faraday‐effect:   c  n B dz  c  n b dz

p
F
e z0
F
e0 z


 




n
 

b
z
  / (c  n dz )
bz  
F
e0
b
z
• For the central chord, is dominated by radial magnetic fluctuations ( ):
br
bz
br ~ bz ~ 2.0  1.7 G
• For the edge chord, a lower bound of can be estimated:
bz
bz  0.6 G
consistent with at at from external coils.
ra
b ~ 0.6 G
Faraday‐effect measurement implies that advection is not enough to ne
account for core and radial compression may be important. 

• Electron continuity equation: ne ~      ne 0  ne 0     
ne Due to advection?
ne ~  r
ne 0
r
ne 0 / r  2  1019 m 4
 r  1.4 103 m
ideal MHD


br ~ ( B ) r  14 G
well above from Faraday‐
br ~ 2.0 G
effect measurements.
Faraday‐effect measurement implies that advection is not enough to ne
account for core and radial compression may be important. 

• Electron continuity equation: ne ~      ne 0  ne 0     
ne Due to advection?
ne ~  r
ne 0
r
ne 0 / r  2  1019 m 4
 r  1.4 103 m
ideal MHD


br ~ ( B ) r  14 G
well above from Faraday‐
br ~ 2.0 G
effect measurements.
ne
Due to radial compression? ne ~ ne 0 ξ
1 
 ξ ~
 r r   
r r
 r ~ 1.5 104 m
ideal MHD


br ~ ( B ) r ~ 1.6 G
br ~ 2.0 G
consistent with from Faraday‐
effect measurements.
Faraday‐effect measurement implies that advection is not enough to ne
account for core and radial compression may be important. 

• Electron continuity equation: ne ~      ne 0  ne 0     
ne Due to advection?
ne ~  r
ne
ne 0
r
ne 0 / r  2  1019 m 4
Due to radial compression? ne ~ ne 0  ξ
1 
 ξ ~
 r r   
r r
 r  1.4 103 m
 r ~ 1.5 104 m
ideal MHD
ideal MHD


br ~ ( B ) r ~ 1.6 G


br ~ ( B ) r  14 G
well above from Faraday‐
br ~ 2.0 G
effect measurements.
br ~ 2.0 G
consistent with from Faraday‐
effect measurements.
Cause of electron density fluctuation requires further exploration.
Outline • MST and Neutral Beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species
‐Dependence on q ‐Nonlinear interaction among multiple modes • Fast‐ion transport
Both super‐ and sub‐Alfvénic fast ions are available by varying beam/plasmas species. 40A & 24kV H‐beam into D‐plasma Super‐Alfvénic:  B    A
30A & 24kV D‐beam into H‐plasma Sub‐Alfvénic:  B    A
• Fast‐ions remain strongly core‐localized as beam species varies.
Frequency pattern of the dominant n=5 mode depends on the fast‐
ion species.
I p  300 kA; ne  0.7  1019 m 3 ; qa  0
H fast‐ion D fast‐ion
Beam Plasma
• EP modes are detected for both super‐ and sub‐Alfvénic fast ions, implying the driving mechanism lies in the real space gradient.
• Multiple frequencies occur with D fast ions compared to single frequency for H fast ions with an increased fluctuation level.
Density fluctuations peak near , feature of continuum mode   k A
destabilized by strong drive.
Line‐integrated density fluctuations  ne dl
H‐beam into H‐plasma
D‐beam into D‐plasma
• Frequency in plasma frame; Doppler shift removed.
Outline • MST and Neutral beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species
‐Dependence on q: connection with resonance condition ‐Nonlinear interaction among multiple mode • Fast‐ion transport
As the safety factor decreases, dominant EP mode transits from n=5 to n=6 and retains m=1.
I p  300 kA; ne  0.7  1019 m 3 ; H beam
• q is tuned by varying reversal parameter F.
• As F decreases, q across the whole minor radius gradually decreases.
q profile
n=5
n=6
Reversal Parameter F
q
rB
RB
Connection with wave‐particle resonance condition
• Wave‐particle resonance condition:
• Fast‐ion safety factor:
q fi 
f
f
f  nf   m  l  f
f  nf   m  l  f / q fi
• q fi required to satisfy resonance condition: q required

fi
ml
n  f / f
Connection with wave‐particle resonance condition
• Wave‐particle resonance condition:
• Fast‐ion safety factor:
q fi 
f
f
f  nf   m  l  f
f  nf   m  l  f / q fi
• q fi required to satisfy resonance condition: q required

fi
•
ml
n  f / f
q fi in RFPs can be quite different from that in tokamaks due to weak Bφ: RFP (24 kV H/D with  /   0.9)
rB
q fi  q 
RFP: RB

q Dfi  q Hfi species dependence
q
rB
RB
rB
q

q

tokamak: fi
RB
Transition from n=5 to n=6 occurs when qfi drops below the required value to satisfy wave‐particle resonance condition.
I p  300 kA; ne  0.7  1019 m 3 ; H beam
• Wave‐particle resonance condition
q Hfi , required

q required
fi
ml
n  f / f
 /   0.9
• For 24 kV H‐ion at
r=0.1 m, q Hfi , required  0.215
n=5
n=6
is required for (1, 5) resonance condition at the measured frequency.
• n‐transition occurs when drops q Hfi
below 0.215 and the (1,5) resonance condition cannot be satisfied.
qfi ‐scan experiments with D fast ions confirm the connection between n‐transition and wave‐particle resonance condition. I p  300 kA; ne  0.7  1019 m 3 ; D beam
• Species dependence
q Dfi  q Hfi
q Dfi , required
• Wave‐particle resonance condition
q required

fi
n=5 dominates
ml
n  f / f
• For 24 kV D‐ion  /   0.9 at r=0.1 m, q Dfi , required  0.22
is required for (1, 5) resonance condition at the measured frequency.
• q Dfi remains above 0.22 and n=5 remains as the dominant EP mode. qmhd
• q fi (not ) is important for wave‐
particle resonance. Outline • MST and Neutral Beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species
‐Dependence on q: connection with resonance condition ‐Nonlinear interaction among multiple modes • Fast‐ion transport
Multiple EP‐modes satisfying three‐wave matching condition are detected.
24kV H‐beam into D‐plasma n=4
f ~ 150kHz
n=10
f ~ 170kHz
n=5
f ~ 85kHz
n=‐1
f ~ 65kHz
f n 5 (85 kHz)  f n  4 (150 kHz)  f n 1 (65 kHz)
f n 10 (170 kHz)  2  f n 5 (85 kHz)
Three‐wave coupling among multiple NBI‐driven modes is observed.
• Stronger n=5 mode occurs prior to weaker n=4 and n=‐1 modes. • Significant bicoherence:  1,4,5 
bn 1bn  4 bn 5
bn 1bn  4
2
2
bn 5
2
• Three‐wave coupling may induce inter‐mode energy transfer and increase damping of the n=5 mode.
Density fluctuations shift outward as the instability transits from the n=5 to n=4 mode. Inboard‐outboard asymmetry is mode dependent.
Outline • MST and Neutral Beam Injector
‐TRANSP modeling of fast‐ion distribution
• Characterization of EP Instabilities: ‐Frequency and mode structure ‐Dependence on fast‐ion/plasma species
‐Dependence on q: connection with resonance condition ‐Nonlinear interaction among multiple mode • Fast‐ion transport
EP instabilities induce fast‐ion transport.
• Neutral particle analyzer: I ANPA
primarily sensitive to core circulating fast ions.
• Neutral particle analyzer signal decreases following NBI‐driven modes, indicating fast‐ion transport.
Instantaneous fast‐ion transport rate is inferred from neutral particle analyzer. • Neutral particle analyzer: I ANPA
• Instantaneous decay rate:  ANPA  
1
I ANPA
dI ANPA
dt
 ANPA   loss  fuel
I ANPA
• For ms , slowly t  0.1
increases from beam‐fueling
 fuel   ANPA  0.4 ms 1
I ANPA
 fuel
 2.5 ms
• Initial onset of the EP modes is ~2.5 ms following the turn‐
on of NBI. Inferred fast‐ion transport rate implies an enhanced fast‐ion transport with the onset of multiple modes. • Instantaneous loss rate: multiple modes
single mode
 loss   fuel   ANPA
• Multiple modes with different spatial structure may provide wave‐particle resonance over a larger minor radius, resulting in stronger fast‐ion transport. Proposed fast‐ion density relaxation process to illustrate a potential EP‐mode excitation sequence.
 peak location • Steep n profile destabilizes  ndl
fi
R  Rmag
the n=5 mode.
Proposed fast‐ion density relaxation process to illustrate a potential EP‐mode excitation sequence.
 peak location • Steep n profile destabilizes  ndl
fi
R  Rmag
the n=5 mode.
• Local flattening of nfi profile steepens the nfi profile near r=0.1 m.
Proposed fast‐ion density relaxation process to illustrate a potential EP‐mode excitation sequence.
 peak location • Steep n profile destabilizes  ndl
fi
R  Rmag
the n=5 mode.
• Local flattening of nfi profile steepens the nfi profile near r=0.1 m.
• Enhanced nfi gradient drives the n=4 and n=‐1 modes. • Multiple modes lead to stronger fast‐ion transport.
Temporal evolution of tearing mode amplitude during the NBI‐
driven modes also indicates fast‐ion transport.
• NBI reduces the amplitude of the innermost‐resonant tearing mode by up to 65%
• Mode‐suppression is lessened following the NBI‐
driven bursts, consistent with fast ion redistribution weakening the suppression effect.
Faraday‐effect polarimetry resolves tearing mode suppression
dynamics‐‐a topic for future studies.
Polarimetry fluctuations   nB

pol
  z dz   nbz dz
Parameterized
fit
with NBI
No NBI
j
innermost core‐resonant (1,5) tearing mode
No NBI
with NBI
br
Tearing mode can impact fast ions and trigger chirping EP modes. m=0, n=1 tearing mode
m=1, n=4 EP mode
Summary
 Energetic‐particle‐driven instabilities in a RFP exhibit:
◦ dynamically‐evolving structure ◦ wave‐particle interactions
◦ nonlinear three‐wave coupling ◦ enhanced fast‐ion transport  First direct measurement of internal magnetic fluctuations associated with EP‐instabilities.
 important parameter for validating MHD modeling
 Fast ions are observed to suppress global tearing modes.
 opportunity to explore interactions between fast ions and MHD instabilities with internal magnetic fluctuation diagnostic. BACKUP SLIDES
Density fluctuations associated with three nonlinearly interacting   k A
EP‐modes (n=4,5,‐1) all peak near .
Line‐integrated density fluctuations
• Frequency in plasma frame; Doppler shift removed.
  k A
n=6 density fluctuation also peaks near .
Line‐integrated density fluctuations
H‐beam into D‐plasma • Frequency in plasma frame; Doppler shift removed.
Faraday‐effect polarimetry measurements suggest that NBI affects plasma current distribution.
I p  300 kA; ne  0.7  1019 m 3 ; qa  0
 pol  cF  ne Bz dz
 J0 
2 
0cF x
x 0
1
 ne f ( r,  )dz
f ( r,  )
where and is shaping factor x  R  R0
for current density profile.
J0 

x
x 0
No NBI: 
 12  1 deg / m
x
With NBI: 
 15  1 deg / m
x
• Faraday rotation measurement suggests that NBI increases central plasma current density by (25±15)%. • Neutral beam current drive remains ambiguous. NBI affects not only equilibrium current distribution but also magnetic fluctuation profile. q  0.2
with NBI
with NBI
No NBI
j
No NBI
• NBI inwardly moves current sheet, consistent with q profile change resulting from the increasing central current density.
No NBI
with NBI
br
Faraday‐effect polarimetry also resolves the detailed tearing mode structure. Polarimetry fluctuations   nB

pol
  z dz   nbz dz
Parameterized
fit
with NBI
No NBI
j
innermost core‐resonant (1,5) tearing mode
No NBI
with NBI
br
Classical modeling predicts that core fast‐ion βf exceeds bulk plasma βbulk and core n f can reach 25% of ne.
n f 0 ~ 25%  ne 0
Core fast‐ion Density 40 A H‐NBI
18ms
ne
18ms injection
nf
18ms injection
fast-ion  f
bulk plasma
bulk
Core nf is expected to be only 8% of ne due to the onset of EP instabilities after 2.5 ms injection. n f 0 ~ 8%  ne 0
Core fast‐ion Density ne
2.5 ms injection
40 A H‐NBI
2.5 ms
nf
2.5 ms injection
fast-ion  f
bulk plasma
bulk

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