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4.8.3 Magnetic and electrostatic deflection of charged particles
Bending radii in magnetic fields
A particle of rest mass m0, momentum p and charge qe, where e is the electron charge and q an integer, that enters a uniform magnetic field, B, perpendicular to its velocity, will describe a circular orbit of radius, R; its ‘magnetic rigidity’, BR, is given by the expression:
Using the particle's rest energy Eo, the kinetic energy Ek and the Lorentz factor γ ≡ 1 + Ek/Eo, the above expression can be re-written as:
or, if Ek/Eo « 1, i.e. in the non-relativistic limit,
In both (la) and (lb), BR is in T·m, Eo and Ek are in MeV and mo is in atomic mass units. See table below for some typical values.
or, in the non-relativistic approximation,
For a particle of velocity v, perpendicular to the field of a parallel-plate deflector of length l, gap d and deflecting potential V, the deflection angle θ is given by:
where the other symbols are defined as before; it is assumed that tan θ θ.
For practical applications:
or, in the non-relativistic limit,
Table of magnetic rigidities, BR (in T·m) for different values of Ek (in MeV)
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