New formulae for the radiation intensity in the Tamm problem

Afanasiev, G. N.; Shilov, V.M.

doi:10.1088/0022-3727/33/22/310

Cited by 10 publications

(8 citation statements)

References 19 publications

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“…In modern experiments, high energy charged particles move through medium almost without energy loss. In this case, one can use either the original Tamm formula (1.1) or its modification for finite observation distances [17,18].…”

Section: Discussionmentioning

confidence: 99%

“…For example, for λ = 4 · 10 −5 cm , L = 1 cm and r = 1 m , the discussed condition reduces to 400 1 , that is, it is greatly violated. The complications arising from the radiation intensity measurements at finite distances and the analytic formulae removing the above drawbacks were discussed in [17,18]. When the conditions 1-3 are fulfilled, the vector potential (3.1) reduces to…”

Section: Necessary Mathematical Formulae and Approximationsmentioning

confidence: 99%

“…Space-time propagation of the shock wave complex mentioned in subsection (4.1) was studied there. In the spectral representation, the decelerated charge motion with the velocity change that is small compared with the velocity itself was studied in [17,22]. Radiation intensities evaluated there have also a plato in the neighbourhood of the Cherenkov angle.…”

Section: Pure Decelerated Charge Motionmentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Necessary Mathematical Formulae and Approximationsmentioning

confidence: 99%

Section: Pure Decelerated Charge Motionmentioning

confidence: 99%

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Numerical and analytical treatment of the smoothed Tamm problem

Afanasiev¹,

Shilov²,

Stepanovsky³

2003

Ann. Phys.

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“…A question arises, why it is needed to use the approximate expression (2.3) although the numerical integration is rather easy [9]. One of the reasons is the same as for the use of the Tamm formula, which does not work properly at realistic distances [8,10]. Despite this fact and due to its remarkable simplicity, the Tamm formula is extensively used by experimentalists for the planning and interpretation of experiments.…”

Section: Main Mathematical Formulaementioning

confidence: 99%

“…This allows us to separate contributions from the uniform and non-uniform parts of a charge trajectory. Formerly, analytic and numerical results for the motion with the velocity change small as compared with the charge velocity itself were obtained in [7,8]. 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.…”

Section: Introductionmentioning

confidence: 99%

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.

show abstract

Numerical and analytical treatment of the smoothed Tamm problem

2003

View full text Add to dashboard Cite

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.

show abstract

New formulae for the radiation intensity in the Tamm problem

Cited by 10 publications

References 19 publications

Numerical and analytical treatment of the smoothed Tamm problem

Numerical and analytical treatment of the smoothed Tamm problem

Cherenkov radiation versus bremsstrahlung in the Tamm problem

Numerical and analytical treatment of the smoothed Tamm problem

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