On the self-consistent algorithm for numerical simulation of the global geomagnetic disturbances and associated electric current spreading to low latitudes

2002 ◽  
Author(s):  
L. Alperorich ◽  
B. Fidel
Keyword(s):  
Numerical Simulation ◽  
Electric Current ◽  
The Self ◽  
Geomagnetic Disturbances ◽  
Current Spreading ◽  
Low Latitudes ◽  
Self Consistent

scholarly journals NUMERICAL SIMULATION OF PLATEAU FORMATION BY AN ELECTRON BUNCH ON THE DISTRIBUTION OF AN ACCELERATING WAKEFIELD IN A PLASMA

2020 ◽  
pp. 47-49
Author(s):  
V.I. Maslov ◽  
R.T. Ovsiannikov ◽  
N. Delerue ◽  
V. Kubytskyi ◽  
I.P. Levchuk ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Electron Bunch ◽  
Plasma Accelerator ◽  
The Self ◽  
Promising Candidate ◽  
Particle In Cell ◽  
The Past ◽  
Self Consistent ◽  
Plasma Accelerators

Over the past decade the production of multi-gigaelectrons from laser-driven and electron-bunch-driven plasma accelerators has been successfully demonstrated. However, applications require improvements of accelerated bunch size and its energy spread. One promising candidate to satisfy these requirements is to externally inject an electron bunch into an electron-bunch-driven plasma accelerator. We present studies on the optimization of the self-consistent distribution of an accelerating wakefield of plateau type, which can lead to improvement of final quality of the externally injected and accelerated electron bunch, using simulations with the particle-in-cell code LCODE. We quantified the effect of the injected bunch density on the plateau formation in the blowout regime.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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