Saturation of multipacting due to space-charge effects in elliptic SRF cavities

Multipacting is a performance-limiting phenomenon in superconducting radio-frequency (SRF) cavities, where the number of secondary electrons emitted from the cavity surface grows due to its periodic collisions with the cavity wall, occurring in resonance with the cavity RF fields. As the number of electrons grows, they experience additional force due to space charge and RF loading due to bunched multipacting current. Most studies on multipacting in SRF cavities ignore these forces and show that the resonant interaction results in exponential growth of the number of multipacting electrons for a range of acceleration gradients, known as the multipacting barrier. When the space charge forces are considered, the exponential growth saturates. In this paper, we study this phenomenon in an elliptic SRF cavity, using a self-developed computer code that offers greater diagnostic capability and improved convergence characteristics compared to available commercial codes. It is explicitly shown that during multipacting, the space charge induced de-bunching leads to particle loss as the multipacting grows, countering the gain of the particles from the secondary emission process due to RF induced bunching. Space charge forces reduce the width of multipacting barrier and lead to multipacting current saturation. The saturated value of total multipacting charge in the cavity has been calculated in this paper as a function of the acceleration gradient. Results obtained using the code are analyzed to provide novel insights into the physics of multipacting saturation and its impact on the performance in SRF elliptic cavities in the presence of space charge and RF loading effects.