Adiabatic Thermal Equilibrium of an Axisymmetric ChargedParticle Beam C' Chen, K' Samokhvalova, and

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Adiabatic Thermal Equilibrium of an Axisymmetric
Charged-Particle BeamC. Chen, K. Samokhvalova,
and J. ZhouPlasma Science and Fusion
CenterMassachusetts Institute of
TechnologySymposium on Recent Advances in
Plasma Physics --- In Celebration of Ronald C.
Davidson's 40 Years of Plasma Physics Research
and Graduate EducationJune 12, 2007
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Thermal rigid-rotor equilibrium in a uniform
magnetic field
Davidson and Krall, 1971
Trivelpiece, 1976
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Applications of high-brightnesscharged-particle
beams

• Large Hadron Collider (LHC)
• Spallation Neutron Source (SNS)
• High Energy Density Physics (HEDP)
• International Linear Collider (ILC)

• Photoinjectors
• High Power Microwave Sources

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Periodic focusing channels
Periodic Quadrupole Field
Periodic Solenoidal Field
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Periodically focused beam equilibria

• Kapchinskij-Vladimirskij (K-V) equilibrium in an
  alternating-gradient (AG) magnetic quadrupole
  focusing channel
• I.M. Kapchinskij, and V. V. Vladimirskij, Proc.
  Int. Conf. High Energy Accel. (CERN, Geneva,
  1959), p. 274
• Delta function distribution in transverse
  energy
• Generalized KV distribution in an axially
  varying, linear focusing channel
• F.J. Sacherer (Ph.D thesis, UC Berkeley, 1968)
• Rigidly rotating equilibrium in a periodic
  solenoidal magnetic focusing field
• C. Chen, R. Pakter and R. C. Davidson, Phys. Rev.
  Lett. 79, 225 (1997)
• KV-like distribution
• Issues
• Non-physical
• Beam halos
• Chaotic-particle motion

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Chaotic phase space in a KV beam
Qian, Davidson and Chen (1994) Pakter, Chen and
Davidson (1999) Zhou, Chen, Qian (2003)
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Thermal equilibrium in a periodic solenoidal
magnetic field

• Experiment Recent experiment at UMER
  demonstrated that the beam focused by a solenoid
  has a bell-shaped profile
• S. Bernal, B. Quinn, M. Reiser, and P.G. OShea,
  PRST-AB 5, 064202 (2002).

New Thermal equilibrium in a periodic solenoidal
magnetic field
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Kinetic and warm-fluid theories
Kinetic theory (Zhou, et al., 2007)
Warm-Fluid Theory (Samokhvalova, et al., 2007)
Equation of state (adiabatic)
Constants of motion
Angular Momentum Generalized Energy
Transverse velocity
Beam density
Distribution function
- constants
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Self-Consistent Density Distribution
Density
Poissons equation
self
2
f
-

Ñ
n
q
p
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b
Beam rotation
Envelope equation
perveance
focusing parameter
rms beam radius
thermal rms emittance
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Beam envelope and beam density
warm beam
cold beam
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UMER edge imaging experiment

• 5 keV electron beam focused by a short solenoid.
• Bell-shaped beam density profiles
• Not KV-like distributions

S. Bernal, B. Quinn, M. Reiser, and P.G. OShea,
PRST-AB, 5, 064202 (2002)
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Density profile comparison for 5 keV, 6.5 mA
electron beam
Experiment
z6.4cm
z11.2cm
z17.2cm
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Conclusion

• Established kinetic and warm-fluid equilibrium
  theories for charged-particle beams in periodic
  solenoidal focusing channels, extending
  Davidsons seminal work on the rigid-rotor
  thermal equilibrium.
• Adiabatic.
• Applicable for both high and low intensities.
• Found excellent agreement between our theory and
  the UMER experiment.
• Future plans
• Study chaotic particle motion and halo formation
  in thermal-equilibrium beams in periodic
  solenoidal focusing channels.
• Establish thermal equilibrium theory of
  charged-particle beams in periodic quadrupole
  focusing channels.
• Develop bunched beam equilibrium theory in rf
  accelerators.
• Pursue high-brightness beam applications.