Optical bremsstrahlung of relativistic particles in a transparent medium and its relation to the Vavilov-čerenkov radiation

Zrelov, V.P.; Růžička, Jan

doi:10.1007/bf01605158

Cited by 18 publications

(23 citation statements)

References 3 publications

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“…Now the paradoxical results of Refs. [12,13], where the Tamm's formulae were investigated numerically become understandable. Their authors attributed the term J Ch in Eqs.…”

Section: Discussionmentioning

confidence: 99%

On Tamm's problem in the Vavilov-Cherenkov radiation theory

Afanasiev

Kartavenko

Stepanovsky

1999

J. Phys. D: Appl. Phys.

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Abstract. We analyse the well-known Tamm problem treating the charge motion on a finite space interval with the velocity exceeding light velocity in medium. By comparing Tamm's formulae with the exact ones we prove that former do not properly describe Cherenkov radiation terms. We also investigate Tamm's formula cos θ = 1/βn defining the position of maximum of the field strengths Fourier components for the infinite uniform motion of a charge. Numerical analysis of the Fourier components of field strengths shows that they have a pronounced maximum at cos θ = 1/βn only for the charge motion on the infinitely small interval. As the latter grows, many maxima appear. For the charge motion on an infinite interval there is infinite number of maxima of the same amplitude. The quantum analysis of Tamm's formula leads to the same results.

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“…Now the paradoxical results of Refs. [12,13], where the Tamm's formulae were investigated numerically become understandable. Their authors attributed the term J Ch in Eqs.…”

Section: Discussionmentioning

confidence: 99%

On Tamm's problem in the Vavilov-Cherenkov radiation theory

Afanasiev

Kartavenko

Stepanovsky

1999

J. Phys. D: Appl. Phys.

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“…It is shown that in the framework of the approximate solution found by Tamm, it is very hard to discriminate between its standard interpretation and one suggested in [4,5]. On the other hand, this discrimination is possible if we treat the Tamm problem simultaneously in the time and frequency representations.…”

Section: Resultsmentioning

confidence: 97%

“…It was shown there that the Cherenkov shock wave (CSW) exists side by side with BS waves and not in any case can be reduced to them. Then, how can this fact be reconciled with the results of [4,5] which describe experimental data quite satisfactorily? The possible explanation of this controversy is that the exact solution obtained in [6] was written out in the space-time representation, while the authors of [4,5] operated with the Tamm formula related to the frequency representation.…”

Section: Introductionmentioning

confidence: 83%

“…[4,5]) in which the radiation described by the Tamm formula was attributed to the interference of BS arising at the start and end of motion.…”

Section: Introductionmentioning

confidence: 99%

“…Unfortunately, the method used there does not work in the treated case, since the charge is accelerated from the state of rest up to acquiring a velocity close to that of light. Numerically, the smoothed Tamm problem with a large velocity change was considered in [9], but the authors did not aim to resolve the above controversy between [4,5] and [6].…”

Section: Introductionmentioning

confidence: 99%

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Cherenkov radiation versus bremsstrahlung in the Tamm problem

Afanasiev¹,

Shilov

2002

J. Phys. D: Appl. Phys.

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The charge motion in medium on a finite space interval is considered. We analyse recent alternative attempts to interpret the radiation described by the Tamm formula as an interference of two instantaneous accelerations arising at the beginning and termination of motion. Exact solution of the Tamm problem in the time representation shows that in some time interval, only the bremsstrahlung shock wave associated with the beginning of motion and the Cherenkov shock wave exist, and there is no bremsstrahlung shock wave associated with the end of motion. This proves that in the time representation the Cherenkov radiation is not necessarily related to the interference of initial and final bremsstrahlung shock waves. In the spectral representation, we consider the motion consisting of accelerated, decelerated, and uniform parts. Analytic formulae are obtained that describe radiation intensities for this motion. Approximating the instantaneous acceleration in the original Tamm problem by the acceleration on a finite path and then tending its length to zero, we prove that the radiation intensity produced on the accelerated part of the charge trajectory also tends to zero (despite the infinite value of acceleration in this limit). This means that in the original Tamm problem the instantaneous acceleration and deceleration do not contribute to the radiation intensity (as it is usually believed). It seems that only the combined consideration of the Tamm problem in the time and spectral representations shows that the above-mentioned alternative interpretation of the Cherenkov radiation fails.

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Numerical and analytical treatment of the smoothed Tamm problem

Afanasiev¹,

Shilov²,

Stepanovsky³

2003

Ann. Phys.

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We study the motion of an electric charge in a medium over a finite spatial distance. We consider at first the motion described by continuous functions of time, that is, its velocity and all its time derivatives are continuous. If the velocity v of the charge is greater than the velocity cn of light in the medium, then the intensity of the radiation is proportional to the frequency in some angular region and decreases exponentially outside of it. If the motion has no jumps in the velocity but jumps in the acceleration, the exponential decrease changes to a reciprocal one with 1/ω . For a purely decelerated motion, when both the initial and the final velocities are greater than cn , the intensity of the radiation contains a plateau. For practical application, the case with a vanishing final charge velocity is important: the intensity of the radiation is then maximal at the Cherenkov angle θc that corresponds to the initial charge velocity whereas it decreases sharply for θ > θc . For this case, provided the velocity of the charge exceeds cn , the total intensity (obtained by integrating the angular intensity of the radiation over the solid angle) is a linear function of the frequency, even though the Tamm condition is strongly violated.

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Optical bremsstrahlung of relativistic particles in a transparent medium and its relation to the Vavilov-čerenkov radiation

Cited by 18 publications

References 3 publications

On Tamm's problem in the Vavilov-Cherenkov radiation theory

On Tamm's problem in the Vavilov-Cherenkov radiation theory

Cherenkov radiation versus bremsstrahlung in the Tamm problem

Numerical and analytical treatment of the smoothed Tamm problem

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