This paper examines the velocity distribution function and cyclotron resonance conditions for a beam of electrons moving in a magnetic field which gradually changes with time. A spatial gradient of magnetic field is known to result in an unstable horseshoe distribution of electrons. The field gradient in time adds additional effects due to an induced electric field. The resultant anisotropic velocity distribution function, which we call a Luvdisk distribution, has some distinctive properties when compared to the horseshoe. Fitting the cyclotron resonance condition circle shows that the frequency of the resultant emission is under the local cyclotron frequency. While the spatial gradient results in the emission coming almost perpendicularly to the field, the direction of the radiation under a time-changing field has more variability. The Luvdisk distribution also arises when the magnetic field has a gradient both in space and time. The beam can be unstable if those gradients are added or subtracted from each other (if the gradients are of equal or different sign), which occurs even when the total change of magnetic field is negative. While the frequency of the emission is related to the final magnetic field value, its direction is indicative of the field’s history which produced the instability.

中文翻译：

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时变磁场中电子束的新动能回旋不稳定性

本文研究了电子束在随时间逐渐变化的磁场中运动的速度分布函数和回旋共振条件。已知磁场的空间梯度会导致电子的不稳定马蹄形分布。由于感应电场，场梯度随时间增加了额外的影响。由此产生的各向异性速度分布函数，我们称之为 Luvdisk 分布，与马蹄形相比具有一些独特的特性。拟合回旋共振条件圆表明合成发射的频率低于局部回旋加速器频率。虽然空间梯度导致发射几乎垂直于场，但时变​​场下的辐射方向具有更大的可变性。当磁场在空间和时间上都具有梯度时，也会出现 Luvdisk 分布。如果这些梯度彼此相加或相减（如果梯度的符号相同或不同），则光束可能不稳定，即使磁场的总变化为负，也会发生这种情况。虽然发射的频率与最终的磁场值有关，但其方向表明了产生不稳定性的磁场历史。