Relativity with Charged Particles & Fluid Approx.

In summary, the conversation discusses using FORTRAN to model the motion of electrons and ions under high voltage potential using a fluid approximation and MHD-like equations. However, the issue of particles exceeding the speed of light arises and the potential solution of replacing m with γm does not work. The expert suggests using the relativistic version of the MHD equations and 4-vectors to fully account for relativistic effects.
  • #1
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Hello community, I'm new here.

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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  • #2
If you wish to fully account for relativistic effects, you will have no choice but to use the relativistic version of the MHD equations; this automatically brings you into the realm of 4-vectors and Minkowski tensors. No way around this, I'm afraid.
 

FAQ: Relativity with Charged Particles & Fluid Approx.

What is relativity with charged particles?

Relativity with charged particles refers to the study of how the motion and behavior of particles with electric charges are affected by the theory of relativity, which describes how objects interact with each other in the presence of gravity.

How does the theory of relativity apply to charged particles?

The theory of relativity states that the laws of physics are the same for all observers, regardless of their relative motion. This applies to charged particles as well, meaning that their behavior and interactions with each other are governed by the same laws of physics regardless of the observer's frame of reference.

What is the fluid approximation in relativity with charged particles?

The fluid approximation is a simplification of the equations used to describe the behavior of a large number of charged particles in a system. It treats the particles as a continuous fluid rather than individual particles, making the calculations easier to manage.

How does relativity with charged particles impact our understanding of the universe?

Relativity with charged particles allows us to study and understand the behavior of particles in extreme environments, such as around black holes or in the early moments of the universe. It also helps us to better understand the fundamental forces and interactions that govern the universe.

What are some practical applications of relativity with charged particles?

Relativity with charged particles has many practical applications, including in the fields of astrophysics, particle accelerators, and nuclear energy. It also plays a crucial role in the development of technologies such as GPS and particle beam therapy for cancer treatment.

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