# Download Aspects of Charged Particle Optics by Peter W. Hawkes (Eds.) PDF

By Peter W. Hawkes (Eds.)

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A matrix description is tried for all these in the approximation retained in this chapter (second order radially, first order axially). Short considerations are given for some analyzers using particular ion optical elements. Finally systems with tandem analyzers are also quoted. 1. Field Free Space The field free spaces ensure much freedom in the choice of the ion optical systems. In the field free space the ion trajectory is a straight line and the nonvanishing matrix elements of the first two rows are: k)= 1, (;) = 1, (+ (:)= (\$) L, (g) L, = = 1, 1, with L the length of this space.

Crossed Fields, Trochoidal Ion Beam A homogeneous magnetic field directed normally to a homogeneous electric field is an ion optical element with interesting focusing properties. It is difficult to connect such an element with others (sometimes a drawback). Its use is restricted by the problems connected with the production of homogeneous electric fields in an extended volume. The fields being directed as in the Fig. 18, the movement equations are: d2y d 2 z eB dy _ -0, m, d t ’ dt2 dt2 - ma dt The integration gives the ion coordinates as function of the time t: d2x dt2 eE (E + uasinca)[ x =3 eB B z = z a + - tE B Y = Y, + vyat eB dz ma -+ ma ( E -- eB B 1 - c o s (mga) ] ) + %eBc o s c a s i n ( z ) , .

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).