By Fritz Rohrlich

Navigable structure. comprises the paper via Spohn (2000) which triggered the writing of this third variation (after forty years).

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Rev. Ser. II, 2, 450 (1913). 3. J. S. Fraser, R. L. Sheffield, E. R. W. Rodenz, IEEE Trans. Nucl. Sci. NS32, 1791 (1985);I. S. Fraper and R. L. Sheffield, IEEE J. QuMrum Elecrmti. 23, 1489 (1987). 4. Reiser, AfP Conference Pmc. 279,579 (1993),ed. J. S. Wurtele. 5. I. Ben-Zvi. Conference Record of the 1993 IEEE Particle Accelerator Conference, 93CH3279-7,p. 2964. 6. R. f PIUC. 139, 1 (1986),ed. Gillespie, Y. Y. Kuo, D. Keefe, and T. P. 1 THE LORENTZ FORCE AND THE EQUATION OF MOTION In this chapter we present a brief review of the methods of relativistic classical dynamics for determining the motion of charged particles in electromagnetic fields.

2964. 6. R. f PIUC. 139, 1 (1986),ed. Gillespie, Y. Y. Kuo, D. Keefe, and T. P. 1 THE LORENTZ FORCE AND THE EQUATION OF MOTION In this chapter we present a brief review of the methods of relativistic classical dynamics for determining the motion of charged particles in electromagnetic fields. We begin with the force on a point charge q in an electromagnetic field, known as the Lorentz force and given by F = q(E +v X 8). 1) Note that the International System of Units (SI), also referred to as the mks system, is used consistently throughout this book.

16) which is the law of conservation of energy in relativistic form. Binomial expansion in the velocity yields ymc2 = me2 (1 = mc’(1 + 51 p2 + 8p4 3 + . * a ) . 17) -p)’R For u 4 c, or /3 4 1, we obtain the nonrelativistic approximation ymc2 - me2 m +v2. 19) which is the famous energy-mass equivalence principle of Einstein’s special -21 THE ENERGY INTEGRAL AND SOME GENERAL FORMULAS relativity theory. 17), which depend on the velocity v , can then be identified as the kinetic energy T. 21) or ET = ymc2 = Eo +T.