Analytical solutions for the energy distribution of charged particles in a weak electric field

1999 ◽  
Vol 6 (4) ◽  
pp. 533-539 ◽  
Author(s):  
G.G.M. Coppa ◽  
A. D'Angola
1962 ◽  
Vol 17 (11) ◽  
pp. 977-989
Author(s):  
R. Chodura ◽  
M. Keilhacker

The following article deals with measurements on hard X-rays produced in thetapinch discharges before breakdown of the gas which often last for several halfcycles of the magnetic field. In order to explain the timedependent intensity and energy of the X-rays, at first two possible spatial distributions of the electric field in a thetapinch-coil are discussed and the gain of energy of charged particles is calculated. The calculation shows that the adiabatic invariant μ = m2 ν2/(2 mo Β) which gives the gain of energy as a function of the magnetic field Β is proportional to (| ω̇g ½to)—3 where ω̇g is the time-derivative of the gyrofrequency which is assumed to be constant and to is the time between zero magnetic field and the start of the particle. Therefore the hard X-rays can be produced only by electrons which were existing in a small time interval around zero magnetic field of the order |ω̇g|–½. Because of the dependence of µ on the initial position of the particle the elecrtons have an energy distribution which is calculated under the assumption that all electrons are uniformely distributed initially over the cross-section of the coil.From the measured time dependence of X-ray intensity the spatial distribution of the electric field in halfcycles before breakdown can be infered. The ratio of the X-ray intensities with and without absorbers has been measured for different values of the timedependent magnetic field and also for different steady bias magnetic fields by which the starting conditions (to) of the particles are altered. These ratios are in good agreement with corresponding theoretical values which are derived from the calculated energy distribution of the electrons. The experimental results show that in halfcycles before breakdown there exist different spatial distributions of the electric field depending on the rising density of charged particles.


1973 ◽  
Vol 34 (4) ◽  
pp. 372-373
Author(s):  
I. K. Kalugina ◽  
I. B. Keirim-Markus ◽  
A. K. Savinskii ◽  
I. V. Filyushkin

2015 ◽  
Vol 26 (49) ◽  
pp. 495201 ◽  
Author(s):  
Ji-Hyun Hur ◽  
Sanghun Jeon

Doklady BGUIR ◽  
2019 ◽  
pp. 21-27
Author(s):  
E. P. Pozhidaev ◽  
T. P. Tkachenko ◽  
A. V. Kuznetsov ◽  
I. N. Kompanets

In a known display cell with the nematic liquid crystal (NLC) and interdigital electrodes on one of the glass substrates, the “In-Plane Switching” (IPS) mode is implemented, in which the NLC main optical axis reorients in a plane parallel to substrates, providing the most correct color reproduction at different angles view, up to 178 ° horizontally and vertically. Unfortunately, the creation of interdigital metal electrodes complicates and increases the technological process cost and causes a decrease in image contrast. At the same time, experimental results and calculations based on classical electro-optics of crystals indicate that electrooptical switching in the IPS mode is a natural and intrinsic feature of a conventional (with continuous electrodes) display cell with a planar-oriented layer of the ferroelectric liquid crystal (FLC), in which the effect of the deformed (by the electric field) helix FLC nanostructure is realized (DHF effect). In such a cell, the reorientation of the main optical axis under the influence of a weak electric field also occurs in the substrate plane if the FLC has a small pitch (about 100 nm or less) and a large tilt angle of molecules in the layer (about 38 ° or more). The dependences of the FLC cell light transmittance measured in this work, confirmed the achievement of the IPS electro-optical mode in the DHF FLC cell; moreover, the light modulation frequency was 1 kHz. Thus, while maintaining all the advantages of the IPS mode known in NLC, its implementation in FLC allows additionally obtaining technological advantages and multiple increase in modulation frequency.


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