By Timothy R. Groves
Charged Particle Optics conception: An advent
identifies an important suggestions of charged particle optics thought, and derives every one mathematically from the 1st rules of physics. Assuming a complicated undergraduate-level figuring out of calculus, this ebook follows a logical development, with every one notion construction upon the previous one. starting with a non-mathematical survey of the optical nature of a charged particle beam, the text:
- Discusses either geometrical and wave optics, in addition to the correspondence among them
- Describes the two-body scattering challenge, that is necessary to the interplay of a quick charged particle with matter
- Introduces electron emission as a realistic outcome of quantum mechanics
- Addresses the Fourier remodel and the linear second-order differential equation
- Includes difficulties to enlarge and fill within the theoretical info, with ideas awarded separately
Charged Particle Optics concept: An Introduction makes an amazing textbook in addition to a handy reference at the theoretical origins of the optics of charged particle beams. it truly is meant to organize the reader to appreciate the big physique of released study during this mature box, with the result translated instantly to sensible application.
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Additional info for Charged Particle Optics Theory
D Qj . 3) This is quite general, since n can take on any positive integral value. For example, a system of N interacting particles has n = 3N degrees of freedom. The central problem of classical mechanics can be stated as follows: given a set of coordinates Qj and velocities Q˙ j at an initial time t0 , calculate the Qj and Q˙ j at any time t. The result of this calculation represents a complete specification of the system. In the present study, we will confine our attention to a single particle of rest mass m and charge q under the influence of electric and magnetic forces.
As this axis need not be a straight line, we designate it a general curvilinear axis. We designate an axial coordinate z, and transverse Cartesian coordinates xj = (x, y) for j = (1, 2) in a plane locally perpendicular to the axis. We further designate ray slope components xj = (x , y ) = dxj /dz. A ray is completely specified at any plane z by its two-vector transverse position x and its two-vector slope x . The central problem in this formulation may be stated as follows: given the transverse position xa and slope xa at an arbitrary starting axial coordinate za , find the transverse position xb and slope xb at an arbitrary ending axial coordinate zb .
42) is identified with an index of refraction for a particle. It depends on the electrostatic potential φ(x) through the momentum p, and depends on the magnetic vector potential A(x) explicitly. The electromagnetic potential varies slowly in space, as governed by Maxwell’s equations. Formulation of the dynamical problem in this way has the advantage that it does not rely on time as an explicit parameter, as long as the potentials are time independent. This greatly simplifies the discussion of geometrical optics for this important class of problems.
Charged Particle Optics Theory by Timothy R. Groves