Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field

Hong Qin; Ronald C. Davidson; Paul J. Channell

Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field

Hong Qin, Ronald C. Davidson, Paul J. Channell

PPPL Computational Science

Research output: Contribution to conference › Paper › peer-review

Abstract

This paper considers an intense nonneutral ion beam propagating in the z-direction through a periodic focusing quadrupole field with transverse focusing force, F_foc = -κ_q(s)(xe_x-ye_y), on the beam ions. A third-order Hamiltonian averaging technique using a canonical transformation is employed to transform away the rapidly oscillating terms. This leads to a Hamiltonian, H(X, Y, X′, Y′, s) = (1/2)(X′²+Y′²)+(1/2)κ_fq (X²+Y²) +ψ(X, Y, s), in the transformed variables (X, Y, X′, Y′), where the focusing coefficient κ_fq is constant, and many solutions and properties of the Vlasov-Maxwell system are well known.

Original language	English (US)
Pages	1629-1631
Number of pages	3
State	Published - 1999
Event	The 18th Biennial Particle Accelerator Conference - New York, NY, USA Duration: Mar 27 1999 → Apr 2 1999

Other

Other	The 18th Biennial Particle Accelerator Conference
City	New York, NY, USA
Period	3/27/99 → 4/2/99

All Science Journal Classification (ASJC) codes

General Engineering

Cite this

@conference{67e7870b05364f7b9a43ee8865175968,

title = "Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field",

abstract = "This paper considers an intense nonneutral ion beam propagating in the z-direction through a periodic focusing quadrupole field with transverse focusing force, Ffoc = -κq(s)(xex-yey), on the beam ions. A third-order Hamiltonian averaging technique using a canonical transformation is employed to transform away the rapidly oscillating terms. This leads to a Hamiltonian, H(X, Y, X′, Y′, s) = (1/2)(X′2+Y′2)+(1/2)κfq (X2+Y2) +ψ(X, Y, s), in the transformed variables (X, Y, X′, Y′), where the focusing coefficient κfq is constant, and many solutions and properties of the Vlasov-Maxwell system are well known.",

author = "Hong Qin and Davidson, \{Ronald C.\} and Channell, \{Paul J.\}",

year = "1999",

language = "English (US)",

pages = "1629--1631",

note = "The 18th Biennial Particle Accelerator Conference ; Conference date: 27-03-1999 Through 02-04-1999",

}

Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field. / Qin, Hong; Davidson, Ronald C.; Channell, Paul J.
1999. 1629-1631 Paper presented at The 18th Biennial Particle Accelerator Conference, New York, NY, USA.

Research output: Contribution to conference › Paper › peer-review

TY - CONF

T1 - Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field

AU - Qin, Hong

AU - Davidson, Ronald C.

AU - Channell, Paul J.

PY - 1999

Y1 - 1999

N2 - This paper considers an intense nonneutral ion beam propagating in the z-direction through a periodic focusing quadrupole field with transverse focusing force, Ffoc = -κq(s)(xex-yey), on the beam ions. A third-order Hamiltonian averaging technique using a canonical transformation is employed to transform away the rapidly oscillating terms. This leads to a Hamiltonian, H(X, Y, X′, Y′, s) = (1/2)(X′2+Y′2)+(1/2)κfq (X2+Y2) +ψ(X, Y, s), in the transformed variables (X, Y, X′, Y′), where the focusing coefficient κfq is constant, and many solutions and properties of the Vlasov-Maxwell system are well known.

AB - This paper considers an intense nonneutral ion beam propagating in the z-direction through a periodic focusing quadrupole field with transverse focusing force, Ffoc = -κq(s)(xex-yey), on the beam ions. A third-order Hamiltonian averaging technique using a canonical transformation is employed to transform away the rapidly oscillating terms. This leads to a Hamiltonian, H(X, Y, X′, Y′, s) = (1/2)(X′2+Y′2)+(1/2)κfq (X2+Y2) +ψ(X, Y, s), in the transformed variables (X, Y, X′, Y′), where the focusing coefficient κfq is constant, and many solutions and properties of the Vlasov-Maxwell system are well known.

UR - https://www.scopus.com/pages/publications/0033347325

UR - https://www.scopus.com/inward/citedby.url?scp=0033347325&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:0033347325

SP - 1629

EP - 1631

T2 - The 18th Biennial Particle Accelerator Conference

Y2 - 27 March 1999 through 2 April 1999

ER -

Periodically-focused solutions to the nonlinear Vlasov-Maxwell equations for intense beam propagation through an alternating-gradient quadrupole field

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