General envelope equation for cylindrically symmetric charged-particle beams

Journal Article · Thu Jul 01 04:00:00 EDT 1976 · Part. Accel.; (United States)

OSTI ID:7142237

Lee, E P; Cooper, R K

An envelope equation, which includes the effects of a solenoidal field, acceleration, self-induced forces, and scattering by a background medium, is derived for the rms radius of a relativistic beam. The system is assumed to be cylindrically symmetric with high enough energy that the paraxial approximation is applicable. The solenoidal field is taken to be uniform normal to the direction of propagation but the beam current profile is arbitrary. The well-known equations of propagation are recovered in their respective domains of applicability (i.e., vacuum transport in a solenoid, equilibrium conditions, the Nordsieck equation, free expansion, and the sausage-mode equation). A treatment is also given of the matching conditions for a beam injected into gas through a foil in the presence of a solenoidal field. The derivation of the envelope equation differs from previous work in making use of the scalar virial moment of the single-particle equation of motion. The beam emittance appears in a natural way as a constant of integration and is shown to be proportional to the effective phase area occupied by the particles. No distribution function is specified for the transverse velocities, but the beam is assumed to pulsate in a self-similar fashion.

• Research Organization: Univ. of California, Livermore
• OSTI ID: 7142237
• Journal Information: Part. Accel.; (United States), Journal Name: Part. Accel.; (United States) Vol. 7:2; ISSN PLACB
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ANGULAR MOMENTUM
BEAM DYNAMICS
BEAM EMITTANCE
BEAM PROFILES
CONFIGURATION
CYLINDRICAL CONFIGURATION
DIFFERENTIAL EQUATIONS
ELECTRIC FIELDS
ENERGY RANGE
EQUATIONS
EQUATIONS OF MOTION
LIMITING VALUES
MAGNETIC FIELDS
NUMERICAL SOLUTION
PULSES
RELATIVISTIC RANGE