Abstract
The effect of multiple scattering (long-range, small-angle elastic Coulomb collisions) on the radiation field associated with transition radiation from a nonstationary plasmalike medium is addressed with the help of a simple model. The model assumes a relativistic charged particle traversing a single medium that is rapidly and abruptly changing its electromagnetic properties. An averaged diffusion tensor is calculated relativistically to effectively approximate a diminished formation zone in the medium, the effect of which on the differential radiation intensity and angular distribution of transition radiation is studied. It is shown here that multiple scattering is more than a fine-tuning effect, in that it has a marked enhancement effect on the differential yield over a wide and significant frequency range of the emitted photons as well as an appreciable shifting and slowing down of the rapid fall of the maximum intensity angular location over an equally significant angular range. It is suggested that one study the effect in an implosion-explosion process of a laser-prepared medium. Implications to transition radiation from a periodic medium and the more general process of transition scattering in nonlinear media are briefly discussed.
I. INTRODUCTION
The processes of transition radiation and transition scattering are phenomena In the case of a relativistic charged particle crossing the interface of two media of differing electromagnetic properties the total radiation measured includes both transition radiation as well as bremsstrahlung.
I. INTRODUCTION
Formal treatments of such problems assume infinite particle trajectories [2 -4] . This assumption often leads to a degree of arbitrariness when separating that portion of radiation associated with transition radiation [5 -8] . However, effects such as multiple scattering can manifest themselves differently upon the competing mechanisms, thus allowing for separation. It is known [5] , for example, that while multiple scattering acts to suppress bremsstrahlung, it actually enhances transition radiation. Earlier treatments [9, 10] of this problem, however, concentrated almost exclusively on the case of a static interface between two media. To highlight the effect of multiple scattering it becomes necessary to bring out and treat explicitly the dynamics in the problem. This can be done by considering a nonstationary plasmalike medium and assuming that over some characteristic time and length the medium changes its electromagnetic properties (dynamic interface) giving rise to transition quanta as relativistic charged particles pass through this interface. In this article we model such a process. In Sec. II we outline the derivation of a simple transition radiation differential intensity formula in this dynamicinterface picture for a plasmalike medium (e.g. , electron liquid in metals). In Sec. III we consider the effect of multiple scattering on the differential intensity and derive a modified intensity formula. In Sec. IV we proceed to analyze this effect. We summarize the problem and our results in Sec. V where we propose to study the effect in an implosion-explosion process of a laser-prepared medium and offer some concluding remarks emphasizing implications to transition radiation from a periodic medium and the more general process of transition scattering in nonlinear media.
II. EMISSION DUE TO DYNAMIC INTERFACE
In our simple model we allow the plasrnalike medium (with characteristic temperature T, charged-particle den-sity po, and dielectric permeability e) to expand freely and isotropically with characteristic thermal expansion velocity PT. We further allow the medium to make a "jump, "
II. EMISSION DUE TO DYNAMIC INTERFACE
parametrized by an abrupt change in the value of e. This jump is defined by a "transition zone" with a time scale and size (b, t, bz). Due to the jump, a change in the parameter nP takes place, n being the index of refraction and P the velocity of the traversing charged particle, upon which, a formation zone appears and photons are emitted [2] . (The formation zone is the distance along the particle trajectory after which the separation between the particle and the emitted photon is on the order of the photon wavelength. ) This formation zone is characterized by (t,l where cu is the emitted photon frequency and 0 is the angle this photon makes with the particle trajectory, to our dynamic-interface picture. Equation (2.3) is for a twomedium process where I, and I are the coherent lengths in vacuum and medium, respectively, given by [5] 4c (2.4) where y is the Lorentz factor of the traversing particle. In essence, l"and l determine the size of the formation zone of the radiation field. The formalism is taken in the relativistic limit neglecting multiple scattering the particle may suff'er during fiight [5] .
II. EMISSION DUE TO DYNAMIC INTERFACE
To check Eq. (2.2), we plot in Fig. 1 To calculate lT, we first calculate the mean chargedparticle density averaged over the size and duration of the transition zone. To that end, we assume our medium has an initial Gaussian distribution for the density [12] r 2/r2 p(r;t =0)=poe unfolding as
II. EMISSION DUE TO DYNAMIC INTERFACE
where r(t)=(ro+P Tt )~and P T=2I3PT. ro can be chosen such that the medium is optically thin and in thermal equilibrium with radiation; by requiring that the bremsstrahlung energy loss rate is much smaller than the black-body rate. For our medium this translates to Tp ))3 X 10 m, which is the limit below which reabsorption of radiation must be taken into account. On 
IV. RESULTS
Before analyzing the effect on the intensity and angular distribution it helps to first isolate the parameter g that parametrizes the diminished formation zone and look at its dependence on the angle and frequency of the emitted photon in the laboratory frame. Plotted in Fig. 2 [14] .
IV. RESULTS
Equations (3.3) -(3.13) offer a simple prescription to estimate the root mean square of the scattering angle in the center-of-mass frame using an averaged diffusion tensor to estimate the dynamical friction the traversing particle experiences due to its interactions with the medium particles. Once this angle is transformed to the laboratory frame it gives a measure [Eq. With this in mind, we plot in Fig. 4 to the angular distribution, plotted in Fig. 5 [16] , the role of multiple scattering may not be of insignificance to the study of transition effects in nonlinear media.

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