M AGNETIC CONFINEMENT We have seen in Section . (see also the box on helical motion of charged particles earlier in this chapter) that orbits of charged particles are helical. If the magnetic field is non-uniform, but does not change much during one circular orbit, then the radius of the helix will decrease as it enters stronger magnetic field and the radius will increase when it enters weaker magnetic fields. We consider two solenoids at a distance from each other, enclosed in an evacuated container (see figure below where we have not shown the container).
Charged particles moving in the region between the two solenoids will start with a small radius. The radius will increase as field decreases and the radius will decrease again as field due to the second solenoid takes over. The solenoids act as a mirror or reflector. [See the direction of F as the particle approaches coil in the figure.
It has a horizontal component against the forward motion.] This makes the particles turn back when they approach the solenoid. Such an arrangement will act like magnetic bottle or magnetic container. The particles will never touch the sides of the container. Such magnetic bottles are of great use in confining the high energy plasma in fusion experiments.
The plasma will destroy any other form of material container because of it’s high temperature. Another useful container is a toroid. Toroids are expected to play a key role in the tokamak , an equipment for plasma confinement in fusion power reactors. There is an international collaboration called the International Thermonuclear Experimental Reactor (ITER), being set up in France, for achieving controlled fusion, of which India is a collaborating nation.
For details of ITER collaboration and the project, you may visit E XAMPLE . Example . A solenoid of length . m has a radius of cm and is made up of turns.
It carries a current of A. What is the magnitude of the magnetic field inside the solenoid? Solution The number of turns per unit length is, . n = turns/m The length l = .
m and radius r = . m. Thus, l / a = i.e., l >> a . Hence, we can use the long solenoid formula, namely, Eq.