By Miklos Szilagyi

The box of electron and ion optics relies at the analogy among geometrical mild optics and the movement of charged debris in electromagnetic fields. The staggering improvement of the electron microscope basically exhibits the chances of snapshot formation via charged debris of wavelength a lot shorter than that of obvious mild. As new purposes similar to particle accelerators, cathode ray tubes, mass and effort spectrometers, microwave tubes, scanning-type analytical tools, heavy beam applied sciences, and so on. emerged, the scope of particle beam optics has been exten­ ded to the formation of excellent probes. The target is to pay attention as many debris as attainable in as small a quantity as attainable. Fabrication of microcircuits is an effective instance of the transforming into value of this box. the present development is in the direction of elevated circuit complexity and development density. as a result of diffraction problem of procedures utilizing optical photons and the technological problems attached with x-ray tactics, charged particle beams have gotten renowned. With them it's attainable to put in writing at once on a wafer lower than laptop keep watch over, with out utilizing a masks. concentrated ion beams provide specially nice probabilities within the submicron quarter. accordingly, electron and ion beam applied sciences will most likely playa extremely important function within the subsequent 20 years or so.

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1-37)]. Then we obtain the Lagrangian in the following scalar form: (2-35) Its partial derivatives are aL _ oq. - rno I ( 1 3 2'2 ) - 1/2 3 '2 ah j 1 - e2L h / q / L h/q/ aq. j~ 1 j ~ 1 . ) These expressions can be rewritten using the components of the momentum p and taking into account Eq. (2-2). We obtain that (2-38) and (2-39 ) 20 2. CHARGED PARTICLES IN ELECTRIC AND MAGNETIC FIELDS Then (2-40) Substituting Eqs. (2-38) and (2-40) into the Lagrangian equations (1-35) we obtain (2-41 ) Here we changed the order of the summations.

The only remaining term will be (v - w) x B. Of course, we also have to substitute the sum of the velocities into the equation of motion (2-1). But the derivative of the constant velocity w is zero, therefore the relative velocity (v-w) will appear on both sides of Eq. (2-1). That means that in the moving coordinate system the particle will have a circular trajectory. The radius of the circle is determined by Eq. (2-137) but the velocity is now the relative velocity, therefore w must be subtracted from its y component.

The long magnetic lens will be considered in more detail in Section 4-10-1-3. 2-7-2-2. Magnetic Deflection. Let us consider a particle moving parallel to the x axis with an initial velocity Vo and entering the idealized homogeneous magnetic field directed parallel to the z axis (Fig. 7) at one of its ends (xo = 0). Its deflection J YL at the other end of the field (x = L) will be determined by Eq. (2-130). We have to substitute v}Q=O, VxO=Vo, and (x-xo)=L. The result is JYL=R[(1-L2/R2)1/2_1J = movo QB [(1- L2Q2B2)1/2 m6v6 -1J (2-146) In accordance with the sign of the Lorentz force, Jy L has a negative value for a positively charged particle (see Fig.

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