Nonlinear third harmonic radiation in thermal free electron laser with modified wiggler

Abstract

Simulation of free electron laser (FEL) with modified wiggler consisting of a conventional planar wiggler with third harmonic field component is presented. A set of self consistent nonlinear differential equations is derived and solved numerically by Runge–Kutta method. The optimum amplitudes of fundamental and third harmonic wiggler filed are obtained to increase the third harmonic radiation in comparison with conventional wiggler and also to have lower electron beam energy compared to conventional wiggler with the same wavelength. For the thermal effect the axial energy spread of electron beam, without any spread in the transverse velocity, is assumed. A peculiar region is found in which there is a sharp increase of the radiation amplitude. Thermal effect of the electron beam was found to be irregular in this peculiar region.

Theoretical Analysis of the Radiation Properties of Some Major X‐Ray Free Electron Lasers

“…It is done by the shimming by ferromagnetic materials and it can enhance the radiation of high harmonics. [66][67][68][69][70][71][72] The measurements of the strength of the field harmonics in these special undulators showed ≈20-30% of the main field amplitude. [70,73,74] In the common planar undulators, used in X-ray FELs, which we will study in what follows, the amplitude of the field harmonic dH 0 is small, d ≲ 0.05.…”

“…[70,73,74] In the common planar undulators, used in X-ray FELs, which we will study in what follows, the amplitude of the field harmonic dH 0 is small, d ≲ 0.05. However, special bi-harmonic undulators exist, where the amplitude of the field harmonic can reach 10-30% of the main field, d ≈ 0.1-0.3; [66][67][68][69][70][71][72][73][74] usually a radiation field of the undulator can be theoretically reproduced by taking into account the first and third field harmonics. [30,31] The effect of the field harmonics on the UR was thoroughly studied in many works, for example, lately it was addressed in refs.…”

Генерация Гармоник В Экспериментах С Лазерами На Свободных Электронах В Рентгеновском Диапазоне --- Теоретический Анализ

“…Однако идеальное синусоидальное магнитное поле не удовлетворяет уравнениям Максвелла во всем пространстве зазора ондулятора, и в реальных устройствах всегда присутствуют высшие гармонические составляющие поля. Кроме того, в ондуляторах с постоянными магнитами иногда специально создают бигармоническое магнитное поле с помощью шиммирования ферромагнитными материалами [15][16][17][18][19][20][21]. Гармоники поля позволяют получить усиленное по сравнению с обычным излучение высших гармоник ОИ [20,22].…”