Plasma physics - single particle in time-varying B-field

In summary, the conversation is about deriving an expression for the drift velocity of a particle in a constant uniform E-field and a slowly time-varying B-field. The person has looked at various resources but has not been able to find the final result and is unsure about how to approach the problem. There is a mention of Faraday's law and magnetic induction, and the possibility of using the adiabatic invariance of the magnetic moment to find the solution. The person believes they have a solution involving an E-cross-B drift term and the adiabatic invariance of the magnetic moment, but is unsure about the exact process.
  • #1
quarky2001
34
0
It's an intro plasma physics course, and already starting to get to me...

I'm asked to derive an expression for the drift velocity of a particle in a constant uniform E-field, and a slowly time-varying B-field.

I've looked at a few books to see if I can even find the final result, so I have an idea what I'm shooting for, but every resource only seems to use the "time-varying B-field" case as a means to talk about the adiabatic invariance of a particles magnetic moment.

Does anyone know how I should be going about this problem? I really have no clue.
 
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  • #2
Does Faraday's law or magnetic induction ring a bell?

Can one find a discussion of E(t) and dB(t)/dt?
 
  • #3
I think I might have come up with a solution, but I'm a bit unsure, as it came about without as much math as I thought it would take.

Given the constant E-field, and the time varying B-field, we know there will be an E-cross-B drift term in the new drift velocity. The other part I think I might be able to get like this:

We know that the magnetic moment is an adiabatic invariant, i.e.

[tex]
\mu = \frac{m{v_\perp}^2}{2B}=constant
[/tex]

And, the phrase "slowly time-varying" in the question suggests to me that this should apply here.

So I should get

[tex]
v_D=\frac{E\times B}{B^2} + ?
[/tex]

I'm just not sure how to arrive at the new term that comes out of the adiabatic invariance of the magnetic moment.
 

1. What is plasma physics?

Plasma physics is the study of charged particles and fluids, including their interactions with electric and magnetic fields. It is an important field of study in understanding the behavior of matter in extreme conditions, such as those found in the sun and other stars.

2. What is a single particle in a time-varying B-field?

A single particle in a time-varying B-field refers to a charged particle, such as an electron or proton, that is experiencing a changing magnetic field over time. This can occur in various situations, such as in a plasma or in experimental setups.

3. How does a single particle in a time-varying B-field behave?

The behavior of a single particle in a time-varying B-field can be complex and is dependent on the properties of the particle, the strength and direction of the magnetic field, and the rate at which the field is changing. In general, the particle will experience a force due to the changing magnetic field, which can cause it to accelerate or change direction.

4. What are the applications of studying single particles in time-varying B-fields?

Studying single particles in time-varying B-fields has many practical applications, including in plasma confinement for fusion energy research, in developing new technologies for particle acceleration, and in understanding the behavior of charged particles in space environments.

5. What are some current research topics in plasma physics related to single particles in time-varying B-fields?

Current research in plasma physics related to single particles in time-varying B-fields includes studying the effects of magnetic turbulence on particle transport, investigating the dynamics of particles in non-uniform magnetic fields, and developing new methods for controlling and manipulating particles in plasmas using time-varying magnetic fields.

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