Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

Lötstedt, Erik

doi:10.1103/physreve.79.026707

Cited by 40 publications

(49 citation statements)

References 53 publications

(143 reference statements)

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“…One is often faced with the problem of calculating strings of Bessel functions whose indices differ by integers [37][38][39]. Recursive algorithms based on the relations…”

Section: Basic Formulasmentioning

confidence: 99%

Numerical calculation of Bessel, Hankel and Airy functions

Lötstedt¹

2012

Computer Physics Communications

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The numerical evaluation of an individual Bessel or Hankel function of large order and large argument is a notoriously problematic issue in physics. Recurrence relations are inefficient when an individual function of high order and argument is to be evaluated. The coefficients in the well-known uniform asymptotic expansions have a complex mathematical structure which involves Airy functions. For Bessel and Hankel functions, we present an adapted algorithm which relies on a combination of three methods: (i) numerical evaluation of Debye polynomials, (ii) calculation of Airy functions with special emphasis on their Stokes lines, and (iii) resummation of the entire uniform asymptotic expansion of the Bessel and Hankel functions by nonlinear sequence transformations.In general, for an evaluation of a special function, we advocate the use of nonlinear sequence transformations in order to bridge the gap between the asymptotic expansion for large argument and the Taylor expansion for small argument ("principle of asymptotic overlap"). This general principle needs to be strongly adapted to the current case, taking into account the complex phase of the argument. Combining the indicated techniques, we observe that it possible to extend the range of applicability of existing algorithms. Numerical examples and reference values are given.

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“…One is often faced with the problem of calculating strings of Bessel functions whose indices differ by integers [37][38][39]. Recursive algorithms based on the relations…”

Section: Basic Formulasmentioning

confidence: 99%

Numerical calculation of Bessel, Hankel and Airy functions

Lötstedt¹

2012

Computer Physics Communications

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“…very high harmonics are generated only at the center of the pulse where the laser intensity-and therefore the argument of the Bessel functions-is largest. For linear laser polarization, we could obtain a similar expansion as (23), but with the expansion coefficients as two-argument Bessel functions [74,75]. While the pre-exponential in the brackets of (24) differ, we note again that its exponential part with the quasi-momentum q µ is equal for linear and circular laser polarization.…”

Section: Separation Of Slow and Fast Time Scales And Higher Harmonicsmentioning

confidence: 86%

Narrowband inverse Compton scattering x-ray sources at high laser intensities

et al. 2015

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Narrowband x-and gamma-ray sources based on the inverse Compton scattering of laser pulses suffer from a limitation of the allowed laser intensity due to the onset of nonlinear effects that increase their bandwidth. It has been suggested that laser pulses with a suitable frequency modulation could compensate this ponderomotive broadening and reduce the bandwidth of the spectral lines, which would allow to operate narrowband Compton sources in the high-intensity regime. In this paper we, therefore, present the theory of nonlinear Compton scattering in a frequency modulated intense laser pulse. We systematically derive the optimal frequency modulation of the laser pulse from the scattering matrix element of nonlinear Compton scattering, taking into account the electron spin and recoil. We show that, for some particular scattering angle, an optimized frequency modulation completely cancels the ponderomotive broadening for all harmonics of the backscattered light. We also explore how sensitive this compensation depends on the electron beam energy spread and emittance, as well as the laser focusing.

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“…For example, for the parameters shown in Fig. 9(b), one can show that the dominant contribution to the matrix element for linear polarization is roughly proportional to the generalized Bessel function A 1 (n, 0, β), which vanishes for even n [43]. However, if the polarization vectors are summed over, then the case of even n contributes, and the curve smoothens out.…”

Section: Comparison To Perturbative Double Compton Scatteringmentioning

confidence: 94%

“…This symmetry can be used for a numerical check of the computer code used for the evaluation, which we have performed in order to reassure ourselves regarding the consistency of the calculations. The gauge symmetry depends sensitively on the Bessel functions and the recurrence relations satisfied by them [43], so that all signs in the formulas have to be right for the symmetry to hold. The gauge symmetry can also be used to simplify the expression, for example, by gauge transforming so that terms proportional to b,c · κ vanish.…”

Section: E Via Gauge Invariance To the Differential Ratementioning

confidence: 99%

Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions

Lötstedt

Jentschura

2009

Phys. Rev. A

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In an intense laser field, an electron may decay by emitting a pair of photons. The two photons emitted during the process, which can be interpreted as a laser-dressed double Compton scattering, remain entangled in a quantifiable way: namely, the so-called concurrence of the photon polarizations gives a gauge-invariant measure of the correlation of the hard gamma rays. We calculate the differential rate and concurrence for a backscattering setup of the electron and photon beam, employing Volkov states and propagators for the electron lines, thus accounting nonperturbatively for the electron-laser interaction. The nonperturbative results are shown to differ significantly compared to those obtained from the usual double Compton scattering.

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Recursive algorithm for arrays of generalized Bessel functions: Numerical access to Dirac-Volkov solutions

Cited by 40 publications

References 53 publications

Numerical calculation of Bessel, Hankel and Airy functions

Numerical calculation of Bessel, Hankel and Airy functions

Narrowband inverse Compton scattering x-ray sources at high laser intensities

Correlated two-photon emission by transitions of Dirac-Volkov states in intense laser fields: QED predictions

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