PHYSICS WITH APPLICATIONS
CONTENTS INTRODUCTION THE TAMM PROBLEM IN THE VAVILOV-CHERENKOV RADIATION THEORY VAVILOV-CHERENKOV RADIATION IN A ?NITE REGION OF SPACE MATHEMATICAL PRELIMINARIES PARTICULAR CASES ORIGINAL TAMM PROBLEM COMPARISON OF THE TAMM AND EXACT SOLUTIONS SPATIAL DISTRIBUTION OF SHOCK WAVES TIME EVOLUTION OF THE ELECTROMAGNETIC ?ELD ON THE SURFACE OF A SPHERE COMPARISON WITH THE TAMM VECTOR POTENTIAL SPATIAL DISTRIBUTION OF FOURIER COMPONENTS QUASI-CLASSICAL APPROXIMATION NUMERICAL CALCULATIONS QUANTUM ANALYSIS OF THE TAMM FORMULA BACK TO THE ORIGINAL TAMM PROBLEM EXACT SOLUTION RESTORING VECTOR POTENTIAL IN THE SPECTRAL REPRESEN- TATION THE TAMM APPROXIMATE SOLUTION CONCRETE EXAMPLE SHOWING THAT THE CSW IS NOT AL- WAYS REDUCED TO THE INTERFERENCE OF BS SHOCK WAVES SCHWINGER’S APPROACH TO THE TAMM PROBLEM INSTANTANEOUS POWER FREQUENCY SPECTRUM INSTANTANEOUS ANGULAR-FREQUENCY DISTRIBUTION OF THE POWER SPECTRUM ANGULAR-FREQUENCY DISTRIBUTION OF THE RADIATED EN- ERGY FOR A ?NITE TIME INTERVAL FREQUENCY DISTRIBUTION OF THE RADIATED ENERGY THE TAMM PROBLEM IN THE SPHERICAL BASIS EXPANSION OF THE TAMM PROBLEM IN TERMS OF THE LEG- ENDRE POLYNOMIALS SHORT R´ESUM´E OF THIS CHAPTER NON-UNIFORM CHARGE MOTION IN A DISPERSION- FREE MEDIUM INTRODUCTION STATEMENT OF THE PHYSICAL PROBLEM SIMPLEST ACCELERATED AND DECELERATED MOTIONS [9] COMPLETELY RELATIVISTIC ACCELERATED AND DECELERATED MOTIONS [11] SMOOTH TAMM PROBLEM IN THE TIME REPRESENTATION MOVING SINGULARITIES OF ELECTROMAGNETIC ?ELD CONCLUDING REMARKS FOR THIS CHAPTER 4 CHERENKOV RADIATION IN A DISPERSIVE MEDIUM ELECTROMAGNETIC POTENTIALS AND ?ELD STRENGTHS TIME-DEPENDENT POLARIZATION OF THE MEDIUM ANOTHER CHOICE OF POLARIZATION ON THE KR¨ONIG-KRAMERS DISPERSION RELATIONS THE ENERGY ?UX AND THE NUMBER OF PHOTONS WKB ESTIMATES CHARGE VELOCITY EXCEEDS THE CRITICAL VELOCITY CHARGE VELOCITY IS SMALLER THAN THE CRITICAL VELOCITY NUMERICAL RESULTS ESTIMATION OF NON-RADIATION TERMS THE IN?UENCE OF THE IMAGINARY PART OF ? 4 10 APPLICATION TO CONCRETE SUBSTANCES 4 10 1 DIELECTRIC PERMITTIVITY (4 7) 4 10 2 DIELECTRIC PERMITTIVITY (4 45) 4 11 1 PARTICULAR CASES 4 11 2 NUMERICAL RESULTS 4 12 SHORT R´ESUM´E OF THIS CHAPTER INFLUENCE OF FINITE OBSERVATIONAL DISTANCES AND CHARGE DECELERATION FINITE OBSERVATIONAL DISTANCES AND SMALL ACCELERATION THE ORIGINAL TAMM APPROACH EXACT ELECTROMAGNETIC ?ELD STRENGTHS AND ANGULAR- FREQUENCY DISTRIBUTION OF THE RADIATED ENERGY APPROXIMATIONS DECELERATED CHARGE MOTION MOTION IN A ?NITE SPATIAL INTERVAL WITH ARBITRARY ACCELERATION MAIN MATHEMATICAL FORMULAE ANALYTIC ESTIMATES THE ABSOLUTELY CONTINUOUS CHARGE MOTION SUPERPOSITION OF UNIFORM AND ACCELERATED MOTIONS SHORT DISCUSSION OF THE SMOOTHED TAMM PROBLEM HISTORICAL REMARKS ON THE VC RADIATION AND BREMSSTRAHLUNG SHORT R´ESUM´E OF CHAPTER 5 RADIATION OF ELECTRIC, MAGNETIC AND TOROIDAL DIPOLES MOVING IN A MEDIUM MATHEMATICAL PRELIMINARIES: EQUIVALENT SOURCES OF THE ELEC- TROMAGNETIC ?ELD A PEDAGOGICAL EXAMPLE: CIRCULAR CURRENT THE ELEMENTARY TOROIDAL SOLENOID ELECTROMAGNETIC ?ELD OF ELECTRIC, MAGNETIC, AND TOROIDAL DIPOLES IN TIME REPRESENTATION ELECTROMAGNETIC ?ELD OF A MOVING POINT-LIKE CURRENT LOOP ELECTROMAGNETIC ?ELD OF A MOVING POINT-LIKE TOROIDAL SOLENOID ELECTROMAGNETIC ?ELD OF A MOVING POINT-LIKE ELECTRIC DIPOLE ELECTROMAGNETIC ?ELD OF INDUCED DIPOLE MOMENTS ELECTROMAGNETIC ?ELD OF ELECTRIC, MAGNETIC, AND TOROIDAL DIPOLES IN THE SPECTRAL REPRESENTATION UNBOUNDED MOTION OF MAGNETIC, TOROIDAL, AND ELECTRIC DIPOLES IN MEDIUM THE TAMM PROBLEM FOR ELECTRIC CHARGE, MAGNETIC, ELECTRIC, AND TOROIDAL DIPOLES ELECTROMAGNETIC ?ELD OF A PRECESSING MAGNETIC DIPOLE DISCUSSION AND CONCLUSION QUESTIONS CONCERNING OBSERVATION OF THE VAVILOV-CHERENKOV RADIATION CHERENKOV RADIATION FROM A CHARGE OF ?NITE DIMENSIONS CHERENKOV RADIATION AS THE ORIGIN OF THE CHARGE DE- CELERATION CHERENKOV RADIATION IN DISPERSIVE MEDIUM RADIATION OF A CHARGE MOVING IN A CYLINDRICAL DIELECTRIC SAMPLE RADIAL ENERGY ?UX ENERGY ?UX ALONG THE MOTION AXIS OPTICAL INTERPRETATION VAVILOV-CHERENKOV AND TRANSITION RADIATIONS FOR A SPHERICAL SAMPLE METALLIC SPHERE DISCUSSION ON THE TRANSITION RADIATION COMMENT ON THE TRANSITION RADIATION COMMENT ON THE TAMM PROBLEM SELECTED PROBLEMS OF THE SYNCHROTRON RADIATION SYNCHROTRON RADIATION IN VACUUM INTRODUCTORY REMARKS ENERGY RADIATED FOR THE PERIOD OF MOTION INSTANTANEOUS DISTRIBUTION OF SYNCHROTRON RADIATION SYNCHROTRON RADIATION IN MEDIUM ELECTROMAGNETIC ?ELD STRENGTHS SINGULARITIES OF ELECTROMAGNETIC ?ELD DIGRESSION ON THE CHERENKOV RADIATION ELECTROMAGNETIC ?ELD IN THE WAVE ZONE CONCLUSION SOME EXPERIMENTAL TRENDS IN THE VAVILOV- CHERENKOV RADIATION THEORY FINE STRUCTURE OF THE VAVILOV-CHERENKOV RADIATION SIMPLE EXPERIMENTS WITH 657 MEV PROTONS MAIN COMPUTATIONAL FORMULAE DISCUSSION CONCLUDING REMARKS TO THIS SECTION OBSERVATION OF ANOMALOUS CHERENKOV RINGS TWO-QUANTUM CHERENKOV E?ECT PEDAGOGICAL EXAMPLE: THE KINEMATICS OF THE ONE-PHOTON CHERENKOV E?ECT THE KINEMATICS OF THE TWO-PHOTON CHERENKOV E?ECT BACK TO THE GENERAL TWO-PHOTON CHERENKOV E?ECT RELATION TO THE CLASSICAL CHERENKOV E?ECT DISCUSSION AND CONCLUSION ON THE TWO-PHOTON CHERENKOV E?ECT