Slab Beam of electrons through Neutralising Ions

In summary, the conversation discusses the calculation of electric and magnetic fields produced by a combination of charges and currents in a region where the thickness of a slab beam of electrons is much smaller than its width. The charge density of the beam is (-ρb), while the neutralizing ions in the channel have a charge density of f*ρb. The goal is to find a value for f where there is no net force on any electron in the beam. The attempt at a solution involves using Biot-Savart's law to calculate the magnetic field produced by the current flowing through the beam. However, there is uncertainty about how to apply this law to the disk of electrons and whether the ions in the channel are moving in the lab frame.
  • #1
Remembrandt
1
0

Homework Statement


A slab beam of electrons of thickness a, width w >> a, charge density
(-ρb ), (Take ρb to be positive.) and velocity vbez passes through a channel of
neutralizing ions with charge density f*ρb where f is some number between zero and one
(all parameters given above apply in the "lab" frame).
  1. Calculate the electric and magnetic fields produced by this combination of charges and currents in the region y << w / 2 .
  2. Find f such that there is no net force on any electron in the beam.

Homework Equations


F[/B] = q(E + v x B)

The Attempt at a Solution


I have an idea as how to begin. But I am not very sure about it.

At any instant of time the new current flowing is given by (ρb - f *ρb)*w*a*vb. If this is the current, then the magnetic field is given by Biot Savarts law (μo/4π)*I/2R ? I just don't get this .

Can anybody guide me on how to start ?
 
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  • #2
I'm not sure what "channel of neutralizing ions" means, but I don't think those ions move in our lab frame.
How did you apply Biot-Savart to your disk of electrons?
 

What is a slab beam of electrons through neutralizing ions?

A slab beam of electrons through neutralizing ions refers to a type of particle accelerator where a beam of electrons is passed through a target of neutralizing ions. This process is used to create a highly concentrated beam of electrons with a specific energy level.

What is the purpose of a slab beam of electrons through neutralizing ions?

The purpose of a slab beam of electrons through neutralizing ions is to create a high energy electron beam that can be used for various applications, such as in research, medical treatments, and industrial processes. The neutralizing ions help to control and stabilize the electron beam, making it more precise and powerful.

How is a slab beam of electrons through neutralizing ions created?

A slab beam of electrons through neutralizing ions is created using a particle accelerator, which is a machine that uses electromagnetic fields to accelerate particles to high speeds. The electrons are first generated through a cathode, then focused and accelerated by electric and magnetic fields until they reach the desired energy level. The neutralizing ions are then introduced to the electron beam to create a more stable and intense beam.

What are the potential applications of a slab beam of electrons through neutralizing ions?

A slab beam of electrons through neutralizing ions has a wide range of potential applications. It can be used in scientific research to study the properties of matter, in medical treatments such as cancer therapy and radiography, and in industrial processes such as sterilization and materials processing. It also has potential uses in space propulsion and nuclear energy.

What are the advantages of using a slab beam of electrons through neutralizing ions?

Using a slab beam of electrons through neutralizing ions has several advantages over other types of particle accelerators. These include a higher beam intensity, more precise control of the electron beam, and lower operating costs. Additionally, the neutralizing ions can help to reduce unwanted effects such as beam instabilities and emittance growth, making the electron beam more stable and reliable for various applications.

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