Brillouin Flow in Relativistic Beams†

Depackh, D. C.; Ulrich, Peter B.

doi:10.1080/00207216108937309

Cited by 14 publications

(3 citation statements)

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“…Equation (9) then allows one to express A z in terms of ', with eq ÀcH =H as the common longitudinal velocity of all beam particles. Therefore, regardless of the density profile across the beam, we find that the longitudinal speed at equilibrium follows a uniform distribution as a function of the radial coordinate [1,7]. Since it is possible to express A z in terms of ', convenient handling of the constant Hamiltonian H defined by expression (1) allows one to write the scalar potential ' entirely in terms of the azimuthal component of the vector potential, 'ðrÞ ¼ '½A ðrÞ.…”

Section: Review Of Equilibrium Statesmentioning

confidence: 93%

“…To address the issue, we simulate the full set of equations (2)- (7). Small perveances are assumed, which implies that the paraxial approximation jdr=dzj ( 1 is valid, as long as emittance is also small enough so as not to push initially paraxial particles into nonparaxial orbits.…”

Section: Numerical Methods For Dynamicsmentioning

confidence: 99%

“…Fully relativistic dynamics has been investigated in the past within the context of beam equilibria [1,[7][8][9]. The present work reviews relativistic beam equilibria from a slightly different perspective and extends the analysis to dynamical states for which we develop the appropriate numerical code.…”

Section: Introductionmentioning

confidence: 96%

See 2 more Smart Citations

Equilibrium and dynamics in the transport of ultrarelativistic charged beams

Nunes

Pakter

Rizzato

et al. 2012

Phys. Rev. ST Accel. Beams

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The present work explores the full role of relativistic effects in the transport of magnetically focused non-neutral cold beams. Not only relativistic effects along the transport axis are discussed, but relativistic effects associated with the transverse particle dynamics are also investigated. Transverse effects are directly connected with the amount of charge the beam transports and a proper discussion of relativistic features should include accurate analysis of all fields self-consistently created by space charge. We review and adapt the equilibrium analysis, and proceed to develop a convenient method to tackle dynamical situations. Simulations revealing how flattop initial conditions, the typical equilibrium profiles of nonrelativistic beams, evolve toward highly nonlinear states in relativistic beams are then presented and discussed.

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Section: Review Of Equilibrium Statesmentioning

confidence: 93%

Section: Numerical Methods For Dynamicsmentioning

confidence: 99%