Sheet beam model for intense space charge: Application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam

Lund, Steven M.; Friedman, A.; Bazouin, G.

doi:10.1103/physrevstab.14.054201

Cited by 4 publications

(10 citation statements)

References 42 publications

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“…Next, in Section 3.3 we study a more applied test case consisting of a mismatched beam in a constant (continous) focusing channel, derived from the 1d sheet beam model developed in Ref. [22].…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…The tune depression σ/σ 0 -defined as the ratio between the phase advance of the particles in the presence and absence of beam charge -can be calculated [22] as…”

Section: Halo Formation In a Mismatched Thermal Sheet Beammentioning

confidence: 99%

“…Note that a correction similar to (11) can be used here to make the deposition conservative, in the sense that ρ n h (x) dx = f n h (z) dz. In the above deposition formula (22), we observe that the evaluation of the "integrated particles" ρn h,k is not straightforward, due to the linear transformation of their shape. To compute them we have considered two methods.…”

Section: Conservative Charge Deposition Schemes For Linearly Transfor...mentioning

confidence: 99%

“…to be specified below. Following the analysis carried out in [22], thermal equilibrium distributions can then be obtained as follows. Given a specific value for the positive, dimensionless parameter…”

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confidence: 99%

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Noiseless Vlasov–Poisson simulations with linearly transformed particles

Pinto

Sonnendrücker

Friedman

et al. 2014

Journal of Computational Physics

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We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts to using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme [J. Denavit, J. Comp. Physics 9, 75 (1972)]. However, it has recently been established [M. Campos Pinto, "Smooth particle methods without smoothing", arXiv:1112.1859 (2012)] that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

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Section: Numerical Simulationsmentioning

confidence: 99%

“…The tune depression σ/σ 0 -defined as the ratio between the phase advance of the particles in the presence and absence of beam charge -can be calculated [22] as…”

Section: Halo Formation In a Mismatched Thermal Sheet Beammentioning

confidence: 99%

Section: Conservative Charge Deposition Schemes For Linearly Transfor...mentioning

confidence: 99%

mentioning

confidence: 99%

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Noiseless Vlasov–Poisson simulations with linearly transformed particles

Pinto

Sonnendrücker

Friedman

et al. 2014

Journal of Computational Physics

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“…The choice of Gaussian b may be appropriate for a neutralized intense beam near a laser-plasma source where a short pulse laser beam typically has a Gaussian-distributed focal spot and the expanding plasma sheath appears to produce an approximately Gaussian beam [30,31]. Conversely, the choice of uniform b may be appropriate for an unneutralized intense beam emerging from a linear transport channel where Debye screening of the linear applied-focusing force leads to an approximately uniform charge-density beam [28,32,33]. The two density profiles are contrasted in Fig.…”

Section: B Beam Modelmentioning

confidence: 99%

Envelope model for passive magnetic focusing of an intense proton or ion beam propagating through thin foils

Lund

Cohen

2013

Phys. Rev. ST Accel. Beams

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Ion beams (including protons) with low emittance and high space-charge intensity can be propagated with normal incidence through a sequence of thin metallic foils separated by vacuum gaps of order the characteristic transverse beam extent to transport/collimate the beam or to focus it to a small transverse spot. Energetic ions have sufficient range to pass through a significant number of thin foils with little energy loss or scattering. The foils reduce the (defocusing) radial electric self-field of the beam while not altering the (focusing) azimuthal magnetic self-field of the beam, thereby allowing passive self-beam focusing if the magnetic field is sufficiently strong relative to the residual electric field. Here we present an envelope model developed to predict the strength of this passive (beam generated) focusing effect under a number of simplifying assumptions including relatively long pulse duration. The envelope model provides a simple criterion for the necessary foil spacing for net focusing and clearly illustrates system focusing properties for either beam collimation (such as injecting a laser-produced proton beam into an accelerator) or for magnetic pinch focusing to a small transverse spot (for beam driven heating of materials). An illustrative example is worked for an idealization of a recently performed laser-produced proton-beam experiment to provide guidance on possible beam focusing and collimation systems. It is found that foils spaced on the order of the characteristic transverse beam size desired can be employed and that envelope divergence of the initial beam entering the foil lens must be suppressed to limit the total number of foils required to practical values for pinch focusing. Relatively modest proton-beam current at 10 MeV kinetic energy can clearly demonstrate strong magnetic pinch focusing achieving a transverse rms extent similar to the foil spacing (20-50 m gaps) in beam propagation distances of tens of mm. This is a surprisingly optimistic result since placing many foils per characteristic beam radius, which one might expect to be necessary to strongly attenuate the self-electric field, would likely result in excessive scattering and loss of focusing from the current neutralization due to the beam propagating too far through solid metal. Results from the envelope model are compared with particle-in-cell simulations to help clarify limits related to envelope-model idealizations. Possible degradations of focusing in situations where strong halo can be generated and where pulse duration is short are clarified.

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