I think this graph shows why my crystalline beam melted.   It plots velocity gradients dvy/dz and dvz/dy (y is horizontal here, z is longitudinal) during the acceleration ramp.   If these are unequal, the beam has angular momentum.   I've found the standard RF acceleration won't change dvz/dy because it gives a constant speed boost irrespective of transverse position, so the two lines get out of sync and the crystal starts spinning.   The "matched" ideal conditions are the diamond "model" points, with both equal.   It eventually spins itself apart, flattening as it does so, as you saw in my earlier animations.   The solution is quite simple: a tiny "crab cavity" but only at about 1/10000 of the voltage of the main cavity (think AA battery) to give the extra twist.   In the final parts of this graph, the velocity gradients get more equal, since angular momentum is mr^2omega and r is increasing from the crystal vaporising, while omega has the same units as the velocity gradients, it gets scaled down.    #physics #accelerators<p><a href='posts/202607/post-20260728-201207-a.png'><img src='posts/202607/post-20260728-201207-a.png' loading='lazy' /></a></p>