Can Mechanically Extended Sources of Radiation in Classical Electrodynamics Solve all Probl.pdfVIP

a r X i v : p h y s i c s / 9 8 0 4 0 0 1 v 3 [ p h y s i c s .c l a s s - p h ] 1 1 N o v 1 9 9 8 CAN MECHANICALLY EXTENDED SOURCES OF RADIATION IN CLASSICAL ELECTRODYNAMICS SOLVE ALL PROBLEMS OF RADIATING POINT-LIKE SOURCES? Alexander A. Vlasov High Energy and Quantum Theory Department of Physics Moscow State University Moscow, 119899 Russia On simple example is shown that a model of mechanically extended source of radiation in classical electrodynamics indeed has some problems with radi- ation reaction force. So one cannot, in general case, state, that the present situation with classical dynamics of mechanically extended sources of radia- tion is ”very satisfactory”. 03.50.De In classical electrodynamics there are known problems of radiation reac- tion force for point-like sources of radiation: preacceleration, runaway and other pathological (unphysical) solutions. In the literature one can find the opinion that if the finite size of a radi- ating source is fully taken into account all the above problems can be solved. In this paper we examine the well known model of ”nonrelativistically rigid charged sphere” to show that nevertheless there remain problems with radiation reaction force. It should be mentioned that ”extended (mechanically) electron models” were proposed long time ago in the works of Abraham, Lorentz, Sommerfeld and others ( for good reviews see, for ex., [1,2,3,4]). Thus in Sommerfeld works [5] was derived the expression of self-force acting on ”nonrelativistically rigid charged sphere”, i.e sphere with radius a, its center moving along trajectory ~R(t), with total charge Q and charge density (in laboratory reference frame) ρ(t, ~r) = Q 4πa2 δ(|~r ? ~R| ? a) . 1 In the case of shell rectilinear motion in [7] was given for the self-force ~Fself = ∫ dV ρ ( ~E + [~v, ~H]/c ) the following expression: Fself = Q2c 4a +1∫ ?1 dx t∫ t1 dt′ ax+ L′ [a2 + 2axL′ + (L′)2]3/2 + Q2 4a +1∫ ?1 dx x? v/c a(1? xv/c) ? Q2 4a +1∫ ?1 dx N1 ? v1/c [a2 + 2axL1 +