Charged particle movement in arbitrary electromagnetic field

In summary, The speaker is an engineer seeking help with developing a simulation code for charged particles moving in an electromagnetic field. They are unsure of how to handle an arbitrary magnetic field vector and have attempted to solve the equations of motion, but are stuck at determining the direction of the magnetic field. They are seeking advice on the next steps and if their solution is correct. Another speaker suggests using the standard aligned equations and a rotation matrix for linear electric and magnetic fields.
  • #1
FlatronL1917
1
0
Hello there! This is my first post here, hopefully I am not posting in the wrong place.
Also, I am an engineer and have not used this stuff for years, so please be patient with me, I am pretty sure that my question is stupid :-)

I would like to develop a simulation code for charged particles moving in a electromagnetic field.
My thought is that, we may not always have the luxury to align the coordinate system to our magnetic field.
Assuming an arbitrary magnetic field vector B in every cell and ignoring the electric field for the moment, I tried solving the equations of motion to see if I can avoid discretization and got the following:

ux = c1x + (c2x+c3x)*cos(qB/m * t) + (c2x-c3x)*sin(qB/m * t)
uy = c1y + (c2y+c3y)*cos(qB/m * t) + (c2y-c3y)*sin(qB/m * t)
uz = c1z + (c2z+c3z)*cos(qB/m * t) + (c2z-c3z)*sin(qB/m * t)

It seems that the cij constants determine the direction of B. I only have the initial conditions for ux, uy, uz, obviously so I can not calculate them. Where do I go from this point? Is my solution wrong? Any help/pointer would be greatly appreciated.
 
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  • #2
It looks like you plane on linear electric and magnetic fields, rather than "arbitrary" ones ... just with axis arbitrarily rotated.

In which case, all you need is the standard aligned equations and the rotation matrix.
 

What is a charged particle?

A charged particle is any particle that carries an electrical charge, either positive or negative. Examples of charged particles include protons, electrons, and ions.

How does a charged particle move in an electromagnetic field?

The movement of a charged particle in an electromagnetic field is determined by the forces acting on it. The particle will experience a force due to its charge interacting with the electric field, and a separate force due to its motion interacting with the magnetic field. The resulting motion is a combination of these two forces.

What is an arbitrary electromagnetic field?

An arbitrary electromagnetic field is a field that is not uniform or constant, meaning that it varies in space and time. This type of field can be created by a variety of sources, such as a moving magnet, an oscillating electric charge, or a changing electrical current.

How is the trajectory of a charged particle in an electromagnetic field calculated?

The trajectory of a charged particle in an electromagnetic field can be calculated using the Lorentz force equation, which takes into account the electric and magnetic forces acting on the particle. This equation can be solved using mathematical techniques such as differential equations or numerical methods.

What is the significance of studying charged particle movement in arbitrary electromagnetic fields?

Studying charged particle movement in arbitrary electromagnetic fields is important in many fields, such as physics, astronomy, and engineering. It allows us to understand the behavior of charged particles in various environments, and can help us develop technologies such as particle accelerators and electric motors.

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