Y. Zhang, H. Boehmer, W.W. Heidbrink, R. McWilliams UC, Irvine,

1
Transport of Fast Ions Modulated by Shear Alfvén
Waves-Through Doppler Shifted Cyclotron
Resonance

• Y. Zhang, H. Boehmer, W.W. Heidbrink, R.
  McWilliams (UC, Irvine),
• T. Carter, S. Vincena, D. Leneman, W. Gekelman,
  P. Pribyl , B. Brugman (UCLA)
• http//hal9000.ps.uci.edu/Presentations.htm
• Work supported by DOE DE-FG02-03ER54720

2
ABSTRACT

• A program to study the interaction of fast ions
  with Alfvén waves is underway at the Large Plasma
  Device (LAPD). We present two experiments1. In
  this one, an antenna launches shear Alfvén waves
  (amplitude dB / B 0.1) in a helium plasma. The
  waves interact with a test particle beam of fast
  ions produced by a Li source3 through the
  Doppler-shifted cyclotron resonance (?Alfvén-
  kzvz OLi). A collimated fast-ion energy
  analyzer measures the non-classical spatial
  spreading of the lithium ions which is
  proportional to the effectiveness of the
  resonance. A resonance spectrum is recovered by
  launching shear Alfvén waves at frequencies from
  0.3 0.8 Oci. Both the magnitude (up to the size
  of the beam radius) and frequency dependence of
  the spreading are in agreement with the
  theoretical prediction using a single particle
  Lorentz code launching fast ions at an ensemble
  of phases relative to the wave. Experimentally
  diagnosed wave magnetic field data is used in the
  simulation. (Here, ?Alfvén and kz are the wave
  frequency and axial wavenumber and vz and OLi are
  the fast-ion axial speed and cyclotron
  frequency.)

1Bull. Am. Phys. Soc., NP8.00014, (2007) 2Y.
Zhang et al., Rev. Sci. Instrum. 78 (2007) 013302.
3
The LArge Plasma Device at UCLA

• Helium Plasma column 0.75 m diameter, 17 m length
• Microwave Interferometers for local Plasma
  density
• (npeak 3 x 1012 /cm3)
• Up to 3.5kG DC Magnetic Field on axis
• Reproducible, 1Hz operation
• Computer Controlled Data Acquisition with maximum
  sampling rate of 100MHz

4
Fast Ion Alfvén resonance Setup
Fast Ion Analyzer z 0.96 m
SAW Antenna z - 3.52 m
Fast Ion Source z 0.00 m
Cathode
Anode
Fast Ion Orbit
B0
LAPD Plasma
?SAW 4 m

• Fast ions complete 3 - 4 gyro-periods before
  collection at Collimated Energy Analyzer (CEA) z
  position
• 600 eV Li beam initial pitch angle at 28o
  relative to B field
• CEA incident angle to match the initial pitch
  angle
• Shear alfven waves (SAW) antenna (15x30 cm)
  generates two interacting SAW channels // B0
• Li beam orbit overlaps partially with SAW for
  wave-particle interaction

5
Landau Resonance VS Doppler Shifted Cyclotron
Resonance
Possible Resonance Experimental Parameters
Of is the fast-ion cyclotron frequency
a) and b) are both experimentally realized
6
Wave increases fast-ion energy and magnetic
moment under resonant condition
Wave phase cosine

• Resonance condition

Fast Ion Gyro-phase cosine
Fast Ion Energy
Magnetic Moment

• An ensemble of orbits with various phase is
  launched. The resultant total r and r?
  displacements at the collection plane from the
  unperturbed orbit indicates the strength of the
  resonance

Fig. Single Particle Simulation of
Doppler-shifted Cyclotron Resonance
7
Simulation Suggests Measurable Displacements
B0
r0? disp.
X wobble
Theoretical Resonance Frequency
r disp.
Y wobble
X wobble
Undisturbed Orbit
Y wobble
Fig2. Phase ensemble XY displacement versus
Fig1. Projection view of a resonant orbit. r
displacement ?V// r0? displacement
?V?
( ,
--plasma Larmor frequency)

• Sharper resonance peak at longer beam travelling
  distance

• r r0? displacements are proportional to SAW
  amplitude

• r r0? displacements are proportional to the
  spatial overlapping of SAW and orbit

8
SAW Induces Spatial Spreading in Addition to
Classical Spreading
Simulation (L. Zhao)
Experiment (RF source)
Fig 1. Orbit geometrical effect is much larger
than classical diffusion when the beam gyro-phase
is not . Our experiments are all designed
to collect beam at integer times of port distance
away from the source
Fig 2. Li beam Classical Spreading Simulation
L. Zhao, W. W. Heidbrink, H. Boehmer, and R.
McWilliams, D. Leneman and S. Vincena, Phys.
Plasmas 12, 052108 (2005)
9
Fast Ion Sources _at_ UC Irvine
0.6 Li Emitter
0.25 Li Emitter
UCI EPM Chamber
0.5 cm Aperture
UC Irvine 0.6 Li Source
Veeco/IONTECH Ar RF-Source
UC Irvine 0.25 Li Source
H. Boehmer, et al, Rev. Sci. Instrum. , Vol. 75,
1013 (2002)
G. Plyushchev, et al, Rev. Sci. Instrum. 77,
10F503 (2006)
Y. Zhang, et al, Rev. Sci. Instrum. , Vol. 78,
013302 (2007)
W.S. Harris, et al, Rev. Sci. Instrum. ,
submitted (2007)
HeatWave labs Inc., www.cathode.com

• As a continuous effort of UC Irvine Fast Ion
  group, various plasma immersible fast ion (1000
  eV) sources have been developed as test particle
  sources in the LAPD plasma.

10
Collimated Energy Analyzer measures
SAW-modulated Fast Ion Signal

• Fast Ion Analyzer records resonant beam signal in
  addition to DC signal
• Maximum resonant signals (SAW frequency) are
  collected around the edge of DC beam profile
• Fast Ion Analyzer rotated to match pitch angle of
  incoming beam

Fast Ion Analyzer
B
Data Collection
Fast Ion Beam
Isolation
-

Typical Thermal Ion Orbit
11
FI Beam Profile Measurement _at_ LAPD

• Contour plots of 0.6 emitter Li-gun beam profile
  in the LAPD plasma (color bars in µA).
• Beam spot collected 1inch away from the source in
  the afterglow
• Beam spot collected 0.32 m away in z direction
  from the source in the afterglow. Initial pitch
  is 28 deg. Gyroradius is 2.8 cm.

• Typical Fast Ion Analyzer collected signal at
  LAPD plasma. Two different time windows (1)
  Discharge. Beam-on (red-dashed) signal is
  compared to beam-off (dashed). Net signal is
  shown as beam-on minus beam-off (2) Afterglow.
  Beam-on (blue) signal is compared to beam-off
  (dashed).

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Antenna and SAW Spatial Pattern Are Chosen to
Accelerate and Decelerate Fast Ions Effectively
Li cyclotron resonance condition b)
Orbit
Vector plot Contour plot
Rectangular Loop antenna (T. Carter, B. Brugman)

• Contour plot measured wave Bx
• Vector plot wave E- calculated from Bx and By

Li-Gun
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Measured Wave Magnetic Field Is Used to Model the
Resonance Interaction
Bx_max
Bx_max
Bx_max
Li cyclotron resonance condition a)
Li cyclotron resonance condition b)
Li cyclotron resonance condition b)
Orbit
Orbit
Orbit
Li-Gun
Li-Gun
Li-Gun
P36, z 1.28 m
P31, z - 0.32 m
P36, z 1.28 m

• It is more favorable that Li Source is farther
  away from wave center
• Wave magnetic field has little damping along the
  distance covered by fast ion
• Actual wave magnetic field is necessary to model
  the Lorentz code

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E Field Calculated from B data
Instantaneous electric field direction determined
from Maxwells quations
Wave electric field determined from the
dispersion relation (KAW)
70 m-1 is determined from perpendicular wave
field pattern
Parallel
Perpendicular
W. Gekelman, S. Vincena, D. Leneman, and J.
Maggs, J. Geophys. Res. 102, 7225 (1997)
N. Palmer, W. Gekelman, and S. Vincena, Phys.
Plasmas 12, 072102 (2005)
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Beam Spot Flattened by SAW w/ Moderate SAW
Amplitude
r0? profile
Li cyclotron resonance condition a)
(Gaussian fitted maximum)
r profile
(?2 weighted average of all radial cuts)
Left Saw-on (solid) beam contour compared with
Saw-off (dashed)
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?r is Modeled by Wobbling Unperturbed Beam
Profile
r r0 ?r sin(?t)
20 change
Li cyclotron resonance condition b)
r0
Radial direction
(best fit determined by least X2 value)
Calculated SAW perturbed profile is
SAW on Fitted
SAW on Data
SAW off Data
where A0 A3 are the coefficients for Gaussian
fits of the unperturbed beam profile
?r 0.3 cm
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Beam Radial Displacement Changes with SAW
Frequency

• Beam radial profile changes according to the
  various frequency drive in the antenna
• Wave field perpendicular profile doesnt change
  significantly for different frequency
• Maximum displacement happens near the theoretical
  resonance frequency

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Case a) Observed Displacement Agrees with
Resonance Theory

• Random error is miniscule Each data point is
  averaged over 4000 samples and 5 individual
  plasma shots.
• The effectiveness of the resonance is recovered
  by the extra spatial spreading of beam with SAW
  on.
• Primary resonance peak is covered by current data
  set
• Simulations with both the experimental wave field
  data and a uniform field within a 10 x 10 cm
  box show a trough at 0.45 ?SAW/?ci and
  secondary peak at 0.35 ?SAW/?ci.

Displacement (cm)
?SAW / ?ci
Red Box ?r Sim. w/ Exp B data Red Tri. ?
r? Sim. w/ Exp B data Blue ?r Sim. w/ box
model B Black Box Experiment results
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Case b) with Double Saw Amplitude Shows Similar
Resonance Pattern

• Primary peak is located again with double the
  displacement
• Resonance is still within linear regime scales
  with wave amplitude
• Discrepancy at higher frequency indicates?
• Box model and experimental field data simulations
  show good agreement on ?r?

Displacement (cm)
?SAW / ?ci
Red Box ?r Sim. w/ Exp B data Red Tri. ?
r? Sim. w/ Exp B data Blue Solid ?r Sim. w/ box
model B Blue Dash ?r? Sim. w/ box model B Black
Box Experiment results
20
Single Particle Energy Gain/Loss at Variable SAW
Frequency
Total Energy
Fast ion perpendicular energy change from 600 eV
Perpendicular Energy
Parallel Energy
?W (eV)
?W- (eV)
? ?
?SAW / ?ci

• 30 eV of energy change is measureable by energy
  analyzer
• At sufficiently large wave amplitude, is phase
  mixing and non-linear effect possible?

Red Diamond ? W- Sim. w/ Exp B data Blue
Solid ? W- Sim. w/ box model B
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Conclusion

• Doppler shifted cyclotron resonance effect is
  observed from the beam spatial non-classical
  spreading with two orbit designs
• Primary resonance peak at SAW frequency 0.65
  ?SAW/?ci, secondary peak 0.35 ?SAW/?ci is
  discovered in experiment and simulation
• Resonance effect is linear to SAW amplitude
• Energy analysis is possible using energy analyzer

22
Future Work

• Fast response circuit to observe SAW frequency
  signal at chosen spatial locations
• Bias fast ion analyzer collector at beam original
  energy ( 600 eV) and observe collected
  population changing at SAW frequqncy
• Energy scan with a fast sweeping voltage source
• Fast particle Trapping in the wave field
• Transport by electrostatic waves
• Defect mode interaction with fast ion?
• Nonlinear heating of fast ion by SAW at multiple
  frequencies

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Shear Alfvén Wave Propagation Gaps in a Magnetic
Mirror Array
Upper Continuum
Lower Continuum
y
Gap
?m
z
SAW Antenna
x
B-dot Probe
Triple Langmuir Probe
SAW
SAW frequency
Yang Zhang, W.W. Heidbrink, H. Boehmer, R.
McWilliams Department of Physics and Astronomy,
University of California, Irvine, California
92697 Guangye Chen Department of Aerospace
Engineering and Engineering Mechanics, University
of Texas, Austin, Texas 78712 Boris N.
Breizman Institute for Fusion Studies, University
of Texas, Austin, Texas 78712 S. Vincena, T.
Carter, D. Leneman, W. Gekelman, P. Pribyl, B.
Brugman Department of Physics and Astronomy,
University of California, Los Angeles, California
90095
http//hal9000.ps.uci.edu/Presentations.htm Work
supported by DOE DE-FG02-03ER54720