Adiabatic Thermal Equilibrium of an Axisymmetric Charged-Particle Beam C. Chen, K. Samokhvalova, and J. Zhou Plasma Science and Fusion Center Massachusetts Institute of Technology Symposium on Recent Advances in Plasma Physics --- In Celebration of Ronald C. Davidson's 40 Years of Plasma Physics Research and Graduate Education June 12, 2007
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Thermal rigid-rotor equilibrium in a uniform magnetic field
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Adiabatic Thermal Equilibrium of an Axisymmetric
Charged-Particle Beam
C. Chen, K. Samokhvalova, and J. Zhou
Plasma Science and Fusion Center
Massachusetts Institute of Technology
Symposium on Recent Advances in Plasma Physics
--- In Celebration of Ronald C. Davidson's 40 Years
of Plasma Physics Research and Graduate Education
June 12, 2007
C. Chen 206/12/07
ce
re
cece
re
re
Thermal rigid-rotor equilibrium in a uniform magnetic field
r
nb(r)
z
Davidson and Krall, 1971
Trivelpiece, 1976
C. Chen 306/12/07
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
C. Chen 406/12/07
Periodic focusing channels
S
S
S
S
N N
N
N
S/2 S/2
I
I
Periodic Quadrupole Field Periodic Solenoidal Field
C. Chen 506/12/07
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)
Qian, Davidson and Chen (1994)Pakter, Chen and Davidson (1999)Zhou, Chen, Qian (2003)
C. Chen 706/12/07
Thermal equilibrium in a periodic solenoidal magnetic field
New: 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. O’Shea, PRST-AB 5, 064202
• 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. O’Shea, PRST-AB, 5, 064202 (2002)
C. Chen 1206/12/07
Density profile comparison for 5 keV, 6.5 mA electron beam
-10 -5 0 5 10x (mm)
0.0
0.5
1.0
1.5
No
rma
lize
d D
en
sity Experiment
Theory
s=6.4 cm
-10 -5 0 5 10x (mm)
0.0
0.5
1.0
1.5
No
rma
lize
d D
en
sity
s=11.2 cm
Experiment
Theory
-10 -5 0 5 10x (mm)
0.0
0.5
1.0
1.5
No
rma
lize
d D
en
sity
s=17.2 cm
Theory
Experiment
Experiment
z=6.4cm z=11.2cm z=17.2cm
C. Chen 1306/12/07
• Established kinetic and warm-fluid equilibrium theories for charged-particle beams in periodic solenoidal focusing channels, extending Davidson’s 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.