scholarly journals A levitated magnetic dipole configuration as a compact charged particle trap

2020 ◽  
Vol 91 (4) ◽  
pp. 043507
Author(s):  
H. Saitoh ◽  
M. R. Stoneking ◽  
T. Sunn Pedersen
Keyword(s):  
Charged Particle ◽  
Magnetic Dipole ◽  
Particle Trap ◽  
Dipole Configuration

5.—Adiabatic Motion in a Charged Particle Trap

1972 ◽  
Vol 70 ◽  
pp. 47-61 ◽  
Author(s):  
J. Byrne
Keyword(s):  
Charged Particle ◽  
Electromagnetic Fields ◽  
Jacobi Equation ◽  
Charged Particles ◽  
Adiabatic Invariants ◽  
Reflection Symmetry ◽  
Adiabatic Conditions ◽  
Adiabatic Motion ◽  
Particle Trap ◽  
Hamilton Jacobi Equation

SynopsisThe adiabatic invariants associated with the motion of charged particles, trapped in electromagnetic fields with rotational and reflection symmetry, have been studied using classical methods based on the Hamilton-Jacobi equation. It has been shown that results, valid for trapping in purely magnetic configurations, may be applied in the analysis of electromagnetic charged particle traps, provided that suitably modified expressions are used for the angular frequencies in the various dynamical modes. Attention is drawn to circumstances in which the adiabatic conditions may be violated because of cancellation of electric and magnetic terms in the equations.

scholarly journals Planar charged-particle trajectories in multipole magnetic fields

1997 ◽  
Vol 15 (2) ◽  
pp. 197-210 ◽  
Author(s):  
D. M. Willis ◽  
A. R. Gardiner ◽  
V. N. Davda ◽  
V. J. Bone
Keyword(s):  
Magnetic Field ◽  
Charged Particle ◽  
Magnetic Dipole ◽  
Equatorial Plane ◽  
Legendre Function ◽  
Neutral Line ◽  
Radial Distance ◽  
Radius Of Curvature ◽  
Particle Trajectories ◽  
Magnetic Neutral Line

Abstract. This paper provides a complete generalization of the classic result that the radius of curvature (ρ) of a charged-particle trajectory confined to the equatorial plane of a magnetic dipole is directly proportional to the cube of the particle's equatorial distance (ϖ) from the dipole (i.e. ρ ∝ ϖ3). Comparable results are derived for the radii of curvature of all possible planar charged-particle trajectories in an individual static magnetic multipole of arbitrary order m and degree n. Such trajectories arise wherever there exists a plane (or planes) such that the multipole magnetic field is locally perpendicular to this plane (or planes), everywhere apart from possibly at a set of magnetic neutral lines. Therefore planar trajectories exist in the equatorial plane of an axisymmetric (m = 0), or zonal, magnetic multipole, provided n is odd: the radius of curvature varies directly as ϖn+2. This result reduces to the classic one in the case of a zonal magnetic dipole (n =1). Planar trajectories exist in 2m meridional planes in the case of the general tesseral (0 < m < n) magnetic multipole. These meridional planes are defined by the 2m roots of the equation cos[m(Φ – Φnm)] = 0, where Φnm = (1/m) arctan (hnm/gnm); gnm and hnm denote the spherical harmonic coefficients. Equatorial planar trajectories also exist if (n – m) is odd. The polar axis (θ = 0,π) of a tesseral magnetic multipole is a magnetic neutral line if m > 1. A further 2m(n – m) neutral lines exist at the intersections of the 2m meridional planes with the (n – m) cones defined by the (n – m) roots of the equation Pnm(cos θ) = 0 in the range 0 < θ < π, where Pnm(cos θ) denotes the associated Legendre function. If (n – m) is odd, one of these cones coincides with the equator and the magnetic field is then perpendicular to the equator everywhere apart from the 2m equatorial neutral lines. The radius of curvature of an equatorial trajectory is directly proportional to ϖn+2 and inversely proportional to cos[m(Φ – Φnm)]. Since this last expression vanishes at the 2m equatorial neutral lines, the radius of curvature becomes infinitely large as the particle approaches any one of these neutral lines. The radius of curvature of a meridional trajectory is directly proportional to rn+2, where r denotes radial distance from the multipole, and inversely proportional to Pnm(cos θ)/sin θ. Hence the radius of curvature becomes infinitely large if the particle approaches the polar magnetic neutral line (m > 1) or any one of the 2m(n – m) neutral lines located at the intersections of the 2m meridional planes with the (n – m) cones. Illustrative particle trajectories, derived by stepwise numerical integration of the exact equations of particle motion, are presented for low-degree (n ≤ 3) magnetic multipoles. These computed particle trajectories clearly demonstrate the "non-adiabatic'' scattering of charged particles at magnetic neutral lines. Brief comments are made on the different regions of phase space defined by regular and irregular trajectories.

Research of the Ionosphere Using Equipment, Placed on Nano-Satellites. Part 1. Modeling a Vacuum Transducer

ANRI ◽  
2020 ◽  
pp. 53-63
Author(s):  
Valeriy Dreyzin ◽  
Ali Nuri Al' Kadimi
Keyword(s):  
Charged Particle ◽  
Charged Particles ◽  
Upper Atmosphere ◽  
Ion Composition ◽  
Vacuum Gauge ◽  
Approximate Design ◽  
Ionization Processes ◽  
Particle Trap ◽  
Positively Charged

The urgency of the task of studying the density and composition of the upper layers of the atmosphere with the help of tools placed in micro- and nano-satellites vehicles is substantiated. A brief description of the structure of the atmosphere is carried out, the relevance and problems of instrumental studies of the density and composition of the upper atmosphere (ionosphere) are shown. A solution to these problems is proposed by developing a combined density and ion composition sensor for the upper atmosphere layers placed on nanosatellites. An approximate design of a compact inverse-magnetron vacuum gauge transducer is proposed, on the basis of which a combined transducer of density and ion composition of the upper atmosphere is constructed by combining it with a charged particle trap. This trap not only ensures the accuracy of its readings, but also allows you to determine the concentration of negatively and positively charged particles. The simulation of ionization processes in the working area of a compact inverse magnetron vacuum gauge transducer is carried out.

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