Intense linear ion accelerators

Kapchinskii, I.M.

doi:10.1070/pu1980v023n12abeh005076

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…The relativistic equation (2) for longitudinal envelopes of a bunch of charged particles moving in a traveling wave fi eld retains all the advantages of the previously derived nonrelativistic equation [1]. It differs advantageously from the known equations for the envelopes fi rst and foremost by simplicity and also by the fact that the solution of Eq.…”

Section: Lagrange Equationmentioning

confidence: 99%

“…Switching from phase to confi guration space, after normalization we obtain the particle density function ρ(x) within a bunch in the form: where x is the longitudinal coordinate measured from the center of the bunch; q and w are, respectively, the longitudinal and transverse semiaxis of an ellipsoid of revolution approximating the bunch; x, z, q, and w, just as all dimensions, are scaled in what follows to the wave length λ; the derivatives are denoted as x´ = dx / dz; ü = dx / dτ; and τ is the dimensionless time, τ = ct / λ. We shall fi nd the kinetic energy of the bunch from the expression for the Hamiltonian [2]. According to this expression, the dimensionless kinetic energy of a relativistic particle can be represented in the form…”

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Longitudinal Dynamics of a Charged-Particle Bunch in a Traveling Wave Field

2015

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and A. V. NesterovichIn this work, which is devoted to the longitudinal dynamics of charged particles in the fi eld of traveling wave, on which the theory of the resonance method of acceleration is based, a transition is made from the dynamics of individual charges to the dynamics of charge bunches as a whole in order to increase the effectiveness of mathematical modeling. A similar problem has already been solved for nonrelativistic bunches. Using the same method, the solution is extended to relativistic bunches. The method is based on the Lagrange equation for the longitudinal motion of a charged-particle bunch in the fi eld of traveling wave; the solutions are the longitudinal size of a bunch and the width of the energy spectrum. The self-fi eld of the bunch is taken into account in the equation and the limitations of linear approximations are eliminated.In the present work, the solution found previously for the problem of the longitudinal dynamics of nonrelativistic bunches of charges in the fi eld of traveling wave is extended to relativistic bunches [1]. The method used is based on the Lagrangian, whose derivation is based on three basic assumptions: the emittance of a bunch can be approximated by an ellipse; the charges in a bunch are distributed uniformly in the region of the emittance; and the bunch itself is approximated in the confi guration space by an ellipsoid of revolution.Lagrangians. We proceed directly to the derivation of the Lagrangian. Let N and M be, respectively, the vertical and horizontal semiaxis of the emittance and N b the number of particles in a bunch uniformly distributed over its emittance, so that the phase density ƒ is constant within a bunch and given by the expressionSpecifi cally, the number of particles in a bunch can be expressed in terms of the pulsed current I of the beam:where λ is the wavelength of the generator powering the accelerating system; Z e is the charge of the particles in the bunch; and c is the speed of light. Switching from phase to confi guration space, after normalization we obtain the particle density function ρ(x) within a bunch in the form:

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Section: Lagrange Equationmentioning

confidence: 99%

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Longitudinal Dynamics of a Charged-Particle Bunch in a Traveling Wave Field

2015

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Muon catalysis and nuclear breeding

Герштейн¹,

Petrov²,

Ponomarev³

1990

Sov. Phys. Usp.

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The optical design of a time-compensated monochromator for high-order harmonic pulses in the extreme-UV (EUV) and soft x-ray regions is presented. The system consists of two grazing-incidence mirrors used as collimating and refocusing elements and two multilayer normal-incidence plane mirrors illuminated in parallel light that rotate along a vertical axis parallel to their planes to select the wavelength, and remain parallel to guarantee the constant direction of the exit beam: this is performed by rotating and translating, at the same time, one of the two mirrors along an axis parallel to the exit direction. The system has constant exit direction in the whole working spectral region. The pulse time duration is not altered up to few femtoseconds. A system operating in the 9-32 nm region is described.

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Hybrid systems for transuranic waste transmutation in nuclear power reactors: state of the art and future prospects

Yurov

Prikhodko

2014

Phys.-Usp.

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Intense linear ion accelerators

Cited by 5 publications

References 3 publications

Longitudinal Dynamics of a Charged-Particle Bunch in a Traveling Wave Field

Longitudinal Dynamics of a Charged-Particle Bunch in a Traveling Wave Field

Muon catalysis and nuclear breeding

Hybrid systems for transuranic waste transmutation in nuclear power reactors: state of the art and future prospects

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