By Peter W. Hawkes (Eds.)
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Extra resources for Aspects of Charged Particle Optics
It is assumed that the electric and magnetic field distributions inside the main field region in the actual system are identical with those generated by closed ideal electrodes and pole faces with axial symmetry. Now, we describe the ion movement in the main part of the crossed fields. In the modified cylindrical coordinate system built around the ion main path of radius p, we write the general expressions of the magnetic B and electric E S FIG. 14. Inhomogeneous electric and magnetic fields, crossed fields, circular main path.
Ue/ui = l/m,uir with I = m,r2d a constant of the movement. Because r = a at the ion entry and exit: bf = Pi. From this the second row of the axial matrix has the elements: (BIB) = 1 and (Ply) = 0, 52 D. IOANOVICIU At first order: y = Or and dO/dz = - l/mar2(z)visin Ei. Then: e, = - 1 mavi sin ei loAz+ - rdi) ei This may be obtained by numerial intergration of r(z). The function r(z) is where f = p cos2 E - 2 ln(r/u). Now we the inverse of z(r) = - K tan E have two more elements for the axial matrix: To derive the radial elements due to the off median plane ion movement we use the radial equation with 8 # 0: The derivative in t is replaced by the derivative in z with the help of the relation: dldt = - v sin E cos pi d/dz.
Parallel Homogeneous Fields The parallel homogeneous electric and magnetic fields were used early in ion analysis. Recently, such analyzers were used in collective acceleration and plasma focusing studies, as reported by Schneider et al. (1985). We consider the two homogeneous constant fields E and B as acting from 40 D. IOANOVICIU Y FIG. 19. Ion distributions along constant mass parabolae produced by parallel electric and magnetic fields. z =O to z = L (Fig. 19). The following movement equations must be integrated: d2x dt2 eE ma’ -- -- d2y e B dz dt2 - m, dt d2z e B dy and -= - - dt2 ma dt Including the initial velocity components, index “i”, the solutions are: We assume that the element with parallel fields is located between two field 41 ION OPTICS free spaces, one of the length L o on the source side, another L , before the observation plane (screen).