Self-consistent study of space-charge-driven coupling resonances

Hofmann, I.; Franchetti, G.

doi:10.1103/physrevstab.9.054202

Cited by 15 publications

(19 citation statements)

References 7 publications

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“…The nonlinear space-charge forces lead to the equipartitioning of energy between the degrees of freedom. The anisotropy leading to coupling resonance [40,41] in the presence of nonlinear space-charge forces was suggested as an approach to the equipartitioning problem [17,28,32]. However, it has been shown that space-charge waves are possible candidates to generate coupling between the degrees of freedom [17,28].…”

Section: Discussionmentioning

confidence: 99%

“…This can be explained, since ξ = η 2 /χ 2 and for our model χ = η, following (2.6) and (2.7) and the definitions of the anisotropic variables. The anisotropy leading to a coupling resonance [40,41] in the presence of nonlinear space-charge forces was suggested as a possible approach to the equipartitioning problem [17,28,32], since collisions are not responsible for the energy transfer in linacs. 6, the quantities χ and η vary in a discontinuous way, which characterizes an anisotropic beam [26,39].…”

Section: Ion Beam Anisotropiesmentioning

confidence: 99%

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Anisotropies in a charged particle beam

Simeoni¹

2009

J. Plasma Phys.

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This paper examines the anisotropies of a charged particle beam moving into a linear focusing channel. Considering a high-intensity ion beam in spacecharge-dominated regime and large mismatched root mean square (RMS) initial beam size, a fast increase in spatial beam anisotropy is observed. Calculations presented here are strong evidence that this anisotropy is responsible for the beam's equipartition. It is shown that particle-particle resonances and wave-particle resonances lead to anisotropization of the beam, i.e. both the envelope and emittance ratios different from unity. It indicates that this anisotropy is responsible for the beam's equipartitioning and suggest that the beam remains equipartitioned even when exhibiting a macroscopic anisotropy, which is characterized by the following properties: the development of an elliptical shape with increasing size along one axis, the presence of a coupling between transversal emittances and halo formation along a preferential direction.

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Section: Discussionmentioning

confidence: 99%

Section: Ion Beam Anisotropiesmentioning

confidence: 99%

Anisotropies in a charged particle beam

Simeoni¹

2009

J. Plasma Phys.

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“…This is described in detail in Refs. [7][8][9][10]. Note that the stopband width increases with space charge (decreasing k xy =k xy0 ) as space charge is the source of the driving term.…”

Section: A Crossing Without Extra Halomentioning

confidence: 98%

“…[8]. Using Ák k 0 À k and the tune ratio k z =k x as variable, the stop-band width can be written in the form k z…”

Section: Semianalytical Scalingsmentioning

confidence: 99%

Halo coupling and cleaning by a space charge resonance in high intensity beams

Hofmann¹

2013

Phys. Rev. ST Accel. Beams

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We show that the difference resonance driven by the space charge pseudo-octupole of high intensity beams not only couples the beam core emittances; it can also lead to emittance exchange in the beam halo, which is of relevance for beam loss in high intensity accelerators. With reference to linear accelerators the ''main resonance'' k z =k x;y ¼ 1 (corresponding to the Montague resonance 2Q x À 2Q y ¼ 0 in circular accelerators) may lead to such a coupling and transfer of halo between planes. Coupling of transverse halo into the longitudinal plane-or vice versa-can occur even if the core (rms) emittances are exactly or nearly equal. This halo argument justifies additional caution in linac design including consideration of avoiding an equipartitioned design. At the same time, however, this mechanism may also qualify as an active dynamical halo cleaning scheme by coupling a halo from the longitudinal plane into the transverse plane, where local scraping is accessible. We present semianalytical emittance coupling rates and show that previously developed linac stability charts for the core can be extended-using the longitudinal to transverse halo emittance ratio-to indicate additional regions where halo coupling could be of importance.

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“…Among these modes, the second order even modes, or envelope modes, are of importance since they can be observed in mismatched beams and may result in the well-known envelope instability [2,7,8]. The second order odd or "skew" modes [2] can drive the resonant emittance exchange by space charge coupling and trigger the "tilting instability" for sufficiently large anisotropy [9][10][11]. More recent studies have revealed that in periodic focusing the second order odd mode can be excited by a parametric instability, likewise a coupled sum mode of two even envelope modes [12,13].…”

Section: Introductionmentioning

confidence: 99%

Modeling of second order space charge driven coherent sum and difference instabilities

Yuan

Hofmann

2017

Phys. Rev. Accel. Beams

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Second order coherent oscillation modes in intense particle beams play an important role for beam stability in linear or circular accelerators. In addition to the well-known second order even envelope modes and their instability, coupled even envelope modes and odd (skew) modes have recently been shown in [Phys. Plasmas 23, 090705 (2016)] to lead to parametric instabilities in periodic focusing lattices with sufficiently different tunes. While this work was partly using the usual envelope equations, partly also particle-in-cell (PIC) simulation, we revisit these modes here and show that the complete set of second order even and odd mode phenomena can be obtained in a unifying approach by using a single set of linearized rms moment equations based on "Chernin's equations." This has the advantage that accurate information on growth rates can be obtained and gathered in a "tune diagram." In periodic focusing we retrieve the parametric sum instabilities of coupled even and of odd modes. The stop bands obtained from these equations are compared with results from PIC simulations for waterbag beams and found to show very good agreement. The "tilting instability" obtained in constant focusing confirms the equivalence of this method with the linearized Vlasov-Poisson system evaluated in second order.

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Self-consistent study of space-charge-driven coupling resonances

Cited by 15 publications

References 7 publications

Anisotropies in a charged particle beam

Anisotropies in a charged particle beam

Halo coupling and cleaning by a space charge resonance in high intensity beams

Modeling of second order space charge driven coherent sum and difference instabilities

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