Charged-Particle Containment in rf-Supplemented Magnetic Mirror Machines

Watson, C. J. H.; Kuo-Petravic, L. G.

doi:10.1103/physrevlett.20.1231

Cited by 22 publications

(9 citation statements)

References 1 publication

(1 reference statement)

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“…where x 0 and y 0 are the unit vectors in the plane perpendicular to the magnetic field B 0 ≈ z 0 B 0 (z), and are smooth on the scale of the oscillations amplitude; Ω = eB 0 /mc is the Larmor frequency. Although µ is often claimed to be an adiabatic invariant (Motz and Watson 1967;Watson and Kuo-Petravic 1968;Eubank 1969), this statement, rather than being proved rigorously, is usually made by analogy with the case of free Larmor rotation at zero rf field (see, though, the discussion in Grebogi et al (1979)). Consequently, conservation of µ is never examined analytically (for numerical and experimental studies, see Eubank (1969) and Watson and Kuo-Petravic (1968)).…”

Section: Introductionmentioning

confidence: 99%

“…Although µ is often claimed to be an adiabatic invariant (Motz and Watson 1967;Watson and Kuo-Petravic 1968;Eubank 1969), this statement, rather than being proved rigorously, is usually made by analogy with the case of free Larmor rotation at zero rf field (see, though, the discussion in Grebogi et al (1979)). Consequently, conservation of µ is never examined analytically (for numerical and experimental studies, see Eubank (1969) and Watson and Kuo-Petravic (1968)). Moreover, it remains unclear exactly what is the nature of the integral (1.2) and what are the approximations under which E can be considered as a conserved quantity.…”

Section: Introductionmentioning

confidence: 99%

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Approximate integrals of radiofrequency-driven particle motion in a magnetic field

Dodin

Fisch

2005

J. Plasma Phys.

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For a particle moving in a non-uniform static magnetic field under the action of a radiofrequency wave, ponderomotive effects result from radiofrequencydriven oscillations nonlinearly coupled with Larmor rotation. Using the Lagrangian and Hamiltonian formalisms, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. These are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the d.c. magnetic field. Under the assumption of non-resonant interaction of the particle with the radiofrequency field, these integrals represent adiabatic invariants of the particle motion.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Approximate integrals of radiofrequency-driven particle motion in a magnetic field

Dodin

Fisch

2005

J. Plasma Phys.

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“…is the new adiabatic invariant proportional to the action of the particle Larmor rotation at frequency Ω 0 = eB/mc, v osc is the induced oscillatory velocity proportional to E [11,93,95,96], and L osc is proportional to E 2 . Suppose B ≈ẑB(z) [Eq.…”

Section: Nonrelativistic Wave Fieldsmentioning

confidence: 99%

Positive and negative effective mass of classical particles in oscillatory and static fields

Dodin

Fisch

2008

Phys. Rev. E

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A classical particle oscillating in an arbitrary high-frequency or static field effectively exhibits a modified rest mass m eff derived from the particle averaged Lagrangian. Relativistic ponderomotive and diamagnetic forces, as well as magnetic drifts, are obtained from the m eff dependence on the guiding center location and velocity. The effective mass is not necessarily positive and can result in backward acceleration when an additional perturbation force is applied. As an example, adiabatic dynamics with m|| > 0 and m|| < 0 is demonstrated for a wave-driven particle along a dc magnetic field, m|| being the effective longitudinal mass derived from m eff . Multiple energy states are realized in this case, yielding up to three branches of m|| for a given magnetic moment and parallel velocity.

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“…Though µ is often claimed to be an adiabatic invariant [2,7,8], this statement, rather than proven rigorously, is usually made by analogy with the case of free Larmor rotation at zero rf field (see though the discussion in [9]). …”

Section: Introductionmentioning

confidence: 99%

“…Consequently, conservation of µ is never examined analytically (for numerical and experimental studies, see [7,8]). …”

Section: Introductionmentioning

confidence: 99%

Approximate Integrals of rf-driven Particle Motion in Magnetic Field

Dodin¹,

Fisch²

2004

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For a particle moving in nonuniform magnetic field under the action of an rf wave, ponderomotive effects result from rf-driven oscillations nonlinearly coupled with Larmor rotation. Using Lagrangian and Hamiltonian formalism, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. Those are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the magnetic field. Under the assumption of nonresonant interaction of the particle with the rf field, these integrals represent adiabatic invariants of the particle motion.

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Charged-Particle Containment in rf-Supplemented Magnetic Mirror Machines

Cited by 22 publications

References 1 publication

Approximate integrals of radiofrequency-driven particle motion in a magnetic field

Approximate integrals of radiofrequency-driven particle motion in a magnetic field

Positive and negative effective mass of classical particles in oscillatory and static fields

Approximate Integrals of rf-driven Particle Motion in Magnetic Field

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