scholarly journals Particle Motion in Longitudinal Waves. I Subluminal Waves

1992 ◽  
Vol 45 (1) ◽  
pp. 1 ◽  
Author(s):  
ET Rowe
Keyword(s):  
Electric Field ◽  
Longitudinal Wave ◽  
Drift Velocity ◽  
Particle Motion ◽  
Equations Of Motion ◽  
Phase Speed ◽  
Relativistic Energy ◽  
Longitudinal Waves ◽  
Arbitrary Phase ◽  
Particle Orbit

The classical equations of motion for a particle moving in a parallel longitudinal wave of arbitrary phase speed are discussed and the case of subluminal waves is considered in detail. Motion of both trapped and untrapped particles is explored with particular reference to the ability of a wave to accelerate particles to relativistic energy. The particle orbit is found in both closed and expanded forms, taking the electric field into account exactly. Expressions are also found for the 'drift velocity' of a particle, which is an important quantity because it is a constant of the particle motion that describes the motion of the centre of oscillation.

scholarly journals Particle Motion in Longitudinal Waves. II Superluminal and Luminal Waves

1992 ◽  
Vol 45 (1) ◽  
pp. 21 ◽  
Author(s):  
ET Rowe
Keyword(s):  
Particle Motion ◽  
Large Amplitude ◽  
Phase Locking ◽  
Charged Particles ◽  
Phase Speed ◽  
Relativistic Effects ◽  
Longitudinal Waves ◽  
Particle Orbits ◽  
Arbitrary Amplitude ◽  
Arbitrary Energy

The motion of charged particles in superluminal and luminal longitudinal waves of arbitrary amplitude is considered in detail, including relativistic effects. In particular we discuss the ability of these waves to accelerate particles. Solutions for the particle orbits are given in both closed form and in terms of relevant expansions. The drift velocity of the particles, which describes the motion of the guiding centre, is identified. Two interesting effects are discovered: (i) the ability of large amplitude superluminal waves to drag particles along at a velocity conjugate to the wave phase speed and (ii) the existence of 'phase locking' particle orbits in the luminal case, in which particles can be accelerated to arbitrary energy.

scholarly journals Development of Calculation Model for Metallic Particle Motion Considering Discharge Phenomenon under High Voltage Electric Field in SF6 Gas

2006 ◽  
Vol 126 (1) ◽  
pp. 73-79
Author(s):  
Toshiaki Rokunohe ◽  
Tomohiro Moriyama ◽  
Yoshitaka Yagihashi ◽  
Makoto Koizumi ◽  
Fumihiro Endo
Keyword(s):  
Electric Field ◽  
High Voltage ◽  
Particle Motion ◽  
Calculation Model ◽  
Metallic Particle

Numerical Investigation of the Coulter Principle in a Microfluidic Device

2013 ◽  
Author(s):  
Muheng Zhang ◽  
Yongsheng Lian
Keyword(s):  
Electric Field ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Navier Stokes ◽  
Working Mechanism ◽  
Navier Stokes Equations ◽  
Sheath Flow ◽  
Coulter Counters ◽  
Pass Through ◽  
Cell Motion

Coulter counters are analytical microfluidic instrument used to measure the size and concentration of biological cells or colloid particles suspended in electrolyte. The underlying working mechanism of Coulter counters is the Coulter principle which relies on the fact that when low-conductive cells pass through an electric field these cells cause disturbances in the measurement (current or voltage). Useful information about these cells can be obtained by analyzing these disturbances if an accurate correlation between the measured disturbances and cell characteristics. In this paper we use computational fluid dynamics method to investigate this correlation. The flow field is described by solving the Navier-Stokes equations, the electric field is represented by a Laplace’s equation in which the conductivity is calculated from the Navier-Stokes equations, and the cell motion is calculated by solving the equations of motion. The accuracy of the code is validated by comparing with analytical solutions. The study is based on a coplanar Coulter counter with three inlets that consist of two sheath flow inlet and one conductive flow inlet. The effects of diffusivity, cell size, sheath flow rate, and cell geometry are discussed in details. The impacts of electrode size, gap between electrodes and electrode location on the measured distribution are also studied.

Attenuation of longitudinal electro-acoustic waves in a plasma

1974 ◽  
Vol 11 (1) ◽  
pp. 37-49
Author(s):  
R. J. Papa ◽  
P. Lindstrom
Keyword(s):  
Dispersion Relation ◽  
Electric Field ◽  
Acoustic Waves ◽  
Collision Frequency ◽  
Wave Dispersion ◽  
Signal Frequency ◽  
Variable Theory ◽  
Longitudinal Waves ◽  
Confluent Hypergeometric Functions ◽  
Linearized Boltzmann Equation

There are several practical situations in partially ionized plasmas when both collisionless (Landau) damping and electron-neutral collisions contribute to the attenuation of longitudinal waves. The longitudinal-wave dispersion relation is derived from Maxwell's equations and the linearized Boltzmann equation, in which electron-neutral collisions are represented by a Bhatnagar–Gross–Krook model that conserves particles locally. (The dispersion relation predicts that, for a given signal frequency ώ), an infinite number of complex wavenumbers kn can exist. Using Fourier–Laplace transform techniques, an integral representation for the electric field of the longitudinal waves is readily derived. Then, using theorems from complex variable theory, a modal expansion of the electric field can be made in terms of an infinite sum of confluent hypergeometric functions, whose arguments are proportional to the complex wavenumbers kn. It is demonstrated numerically that the spatial integral of the square of the electric field amplitude decreases as the electron-neutral collision frequency increases. Also, the amount of energy contained in the first few (lowest) modes, and the coupling between the modes, is examined as a function of plasma frequency, signal frequency and collision frequency.

Electron drift velocity versus electric field in GaAs

1986 ◽  
Vol 29 (12) ◽  
pp. 1295-1296 ◽  
Author(s):  
Chian S. Chang ◽  
Harold R. Fetterman
Keyword(s):  
Electric Field ◽  
Drift Velocity ◽  
Electron Drift Velocity ◽  
Velocity Versus ◽  
Electron Drift

Ion acceleration by multiple laser pulses and their spontaneous electromagnetic fields in plasma

2008 ◽  
Vol 74 (1) ◽  
pp. 111-118
Author(s):  
FEN-CE CHEN
Keyword(s):  
Magnetic Fields ◽  
Electric Field ◽  
Analytical Model ◽  
Electromagnetic Fields ◽  
Equations Of Motion ◽  
Charged Particles ◽  
Laser Pulses ◽  
The Self ◽  
Electric And Magnetic Fields ◽  
Relativistic Equations

AbstractThe acceleration of ions by multiple laser pulses and their spontaneously generated electric and magnetic fields is investigated by using an analytical model for the latter. The relativistic equations of motion of test charged particles are solved numerically. It is found that the self-generated axial electric field plays an important role in the acceleration, and the energy of heavy test ions can reach several gigaelectronvolts.

Radial component of vortex electric field force

2021 ◽  
Vol 11 (1) ◽  
pp. 32-35
Author(s):  
Vasyl Tchaban ◽  
Keyword(s):  
Electric Field ◽  
Equations Of Motion ◽  
Spherical Body ◽  
Radial Component ◽  
Force Interaction ◽  
Finite Speed ◽  
The Third ◽  
Electric Field Force ◽  
Electrically Charged ◽  
Positively Charged

he differential equations of motion of electrically charged bodies in an uneven vortex electric field at all possible range of velocities are obtained in the article. In the force interaction, in addition to the two components – the Coulomb and Lorentz forces – the third component of a hitherto unknown force is involved. This component turned out to play a crucial role in the dynamics of movement. The equations are written in the usual 3D Euclidean space and physical time.This takes into account the finite speed of electric field propagation and the law of electric charge conservation. On this basis, the trajectory of the electron in an uneven electric field generated by a positively charged spherical body is simulated. The equations of motion are written in vector and coordinate forms. A physical interpretation of the obtained mathematical results is given. Examples of simulations are given.

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