Differential Geometry Relations, relating to plasma physics.

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SUMMARY

The discussion focuses on the differential geometry relationship between the derivatives dE/dx, dE/dy, and dE/dt in the context of plasma physics, specifically regarding straggling. It highlights that while there is no universal differential geometry relation applicable without knowing the specific geometry of the plasma, physical relations exist that depend on the charge state of the plasma. The conversation emphasizes the need for clarity in understanding these relationships, which are often presented abstractly in existing resources.

PREREQUISITES
  • Understanding of differential geometry concepts
  • Familiarity with plasma physics principles
  • Knowledge of kinetic energy equations in particle physics
  • Basic grasp of derivatives and their physical interpretations
NEXT STEPS
  • Research specific differential geometry applications in plasma physics
  • Explore the effects of charge states on plasma behavior
  • Study the mathematical formulation of kinetic energy in particle interactions
  • Investigate resources in physics forums for practical examples of these relationships
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Researchers in plasma physics, physicists specializing in differential geometry, and students seeking to understand the mathematical relationships governing particle behavior in plasma environments.

Alexjcb
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The context of this question is looking at straggling in plasma. I was told there was a simple differential geometry relationship between the following entities:

dE/dx, dE/dy and dE/dt,

where x,y are distance in perpendicular directions (axes on a plane), t is time and I'm using E to denote mean kinetic energy of a particle.

So far the resources I've consulted don't show in a clear manner how to go about finding this relation, they remain in the abstract.
 
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There is no "differential geometry" relation, unless you happen to know the specific geometry of the plasma but there are physical relations depending upon whether the plasma is charged or not.

You might get better answers posting this question in the "physics section".
 

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