ELECTROMAGNETIC SEPARATION OF ISOTOPES IN A MAGNETIC FIELD.

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Let us consider the beam of particles of mass m and of charge q which move with equal velocity V. In a magnetic field B these particles are acted upon by a force of Lorentz: F = (q/c)[V,B] (in Gauss system of units). Under the action of this force the particle will move in a circle path of radius R = (mc/qB)V.  So, the particles of different masses will follow paths bent on different radii. This principle is used to separate the isotopes - the particles of the same charge, but a little bit different masses.

Instead of parallel  beam of the particles moving with the equal velocity, we can use paraxial beam of particles of equal energy. If the aperture of the beam is rather small then after a half of the circle the particles will meet in a point. Before the particles enter the magnetic field they are accelerated in a electrostatic field. If the potential difference is U, then the velocity of the particles will be V=√2eU/m . Moving in a magnetic field the particles will be acted upon the force of Lorentz F = mV²/R = (e/c)VB. From this equation we can find the radius of the trajectory R=(c/B)√2Um/q. So, we can see that the distance from the slot (source of particles) to the point of focusing is proportional to √m/q . Width of the focus for every type of isotope  δ = R·sin²(φ/2) ≈ Rφ²/4, where φ is the angle aperture of the particles beam.