Terrestrial Gamma ray Flashes exhibit slopes of ionizing radiation associated with bremsstrahlung. Bremsstrahlung has a continuous spectrum of radiation from radio waves to ionizing radiation. The Poynting vector of the emitted radiation, that is, the radiation pattern around a single particle under the external lightning electric field during interaction with other particles or atoms, is not quite well known. The overall radiation pattern arises from the combination of radiation of parallel and perpendicular motions of a particle caused by the acceleration from the lightning electric field and the bremsstrahlung. The calculations and displays of radiation patterns are generally limited to a low-frequency approximation for radio waves and separate parallel and perpendicular motions. Here, we report the radiation patterns of combined parallel and perpendicular motions from accelerated relativistic particles at low and high frequencies of the bremsstrahlung process with an external lightning electric field. The primary outcome is that radiation patterns have four relative maxima with two forward peaking and two backward peaking lobes. The asymmetry of the radiation pattern, that is, the different intensities of forward and backward peaking lobes, are caused by the Doppler effect. A novel outcome is that bremsstrahlung has an asymmetry of the four maxima around the velocity vector caused by the curvature of the particle's trajectory as it emits radiation. This mathematical modeling helps to better understand the physical processes of a single particle's radiation pattern, which might assist the interpretation of observations with networks of radio receivers and arrays of γ-ray detectors.

中文翻译：

---

闪电先导电场加速的相对论粒子的非对称后向峰值辐射模式

地面伽马射线闪光表现出与轫致辐射相关的电离辐射斜率。轫致辐射具有从无线电波到电离辐射的连续辐射谱。发射辐射的坡印廷矢量，即在与其他粒子或原子相互作用期间，在外部闪电电场下单个粒子周围的辐射模式，还不是很清楚。整个辐射模式是由闪电电场和韧致辐射加速引起的粒子平行和垂直运动的辐射组合产生的。辐射图的计算和显示通常仅限于无线电波的低频近似以及分离的平行和垂直运动。这里，我们报告了在具有外部闪电电场的韧致辐射过程的低频和高频下，来自加速相对论粒子的组合平行和垂直运动的辐射模式。主要结果是辐射模式有四个相对最大值，两个前向峰值和两个后向峰值波瓣。辐射方向图的不对称性，即前向和后向尖峰波瓣的强度不同，是由多普勒效应引起的。一个新的结果是，韧致辐射在速度矢量周围的四个最大值不对称，这是由粒子发射辐射时的轨迹曲率引起的。这种数学模型有助于更好地了解单个粒子辐射模式的物理过程，γ射线探测器。