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I'm using FORTRAN to model the motion of electrons and ions when accelerated under a high voltage potential. I'm using a fluid approximation and MHD-like equations (conservation of mass, energy, momentum) and a finite volumes numerical method to solve the equations.

The thing is that when the electron density is high, the particles' speed exceed the speed of light. I thought that replacing m with γm would fix the problem, at least as a first-order approximation, but it didn't. I'm afraid I need to replace everything with its corresponding 4-vector but this requires a complete rewrite of the program from start.

Any ideas?

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# Relativity with charged particles and fluid approximation

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