“How to accelerate charged particle in magnetic field”
Aims and objectives
For the proposed research we will be using classical equations that are related to magnetic moment in moving charged particles. The radiation reaction will also be incorporated in this experimental study. Classical equations used will be Landau-Lifshitz equations which is specified for spinless case. This is a special case that involves spin-polarized motion in steady magnetic field. The aim of the research is to analyse that a particle moving in the magnetic field does looses energy (Moncrief, 1980).
Following are the objectives of the research that will be taken into consideration:
We propose classical equations of motion for a charged particle with magnetic moment.
We account for radiation reaction as well.
Unlike previous proposals we do not have runaway solutions.
This research is important in order to determine the situation of the magnetic field and the particle that moving on the magnetic field. How the energy in the particle is related to the magnetic field and what causes the loss in energy (Moncrief, 1980: 333).
The magnetic induction accelerator, or betatron, belongs to the group of machines designed to accelerate charged particles to high energies. It was invented in 1941 by Donald W. Kerst. The betatron built in 1945 accelerated electrons to an energy of 10 8 eV.
The accelerator consisted of a toroidal tube which had been evacuated and is placed between the pole pieces of an electromagnet. The electrons, accelerated through a potential difference of about 50,000 volts by an electron gun, entered tangentially into the tube, where the magnetic field made them spin in a circular orbit of 5 m in length. Betatrons used for studying certain types of nuclear reactions and as a source of radiation for cancer treatment (Kryvdyk, 1999: 593).
The force exerted by the magnetic field, as we have seen in the mass spectrometer and the cyclotron particle forces to describe a circular orbit. The problem that arises in this situation is that as the particles are accelerated, they need a magnetic field for increasing the particles describe a circular orbit of a given radius.
The physics of betatron combined, the Faraday law , and the motion of charged particles in an electric field and a magnetic field .
First, determine the electric field at each point in space produced by a magnetic field having axial symmetry (the module depends only on the distance r to the Z axis), but in turn, changes with time. The chosen closed path is a circle of radius r, centered on the axis Z. As the flow varies with time, it induces an emf given by Faraday's law
Due to the axial symmetry, the generated electric field E r depends only, and is constant in all the points tangent to the circle of radius r, such that V = E 2 p · r
(Kryvdyk, 1998: 475)
The magnetic field flux is F = p r 2. Where is the mean field exists in the region covering the area S = p r 2. Clearing the electric field module
Movement of charged particles
Since the particle describes a circular path with variable speed over time, we study the motion of the particle in the tangential direction and the normal direction