Challenges in Understanding Space Charge Effects

Space charge effects in high intensity and high brightness synchrotrons can lead to undesired beam emittance growth, beam halo formation and particle loss. A series of dedicated machine experiments has been performed over the past decade in order to study these effects in the particular regime of long-term beam storage ($10^5$-$10^6$ turns) as required for certain applications. This paper gives an overview of the present understanding of the underlying beam dynamics mechanisms. In particular it focuses on the space charge induced periodic resonance crossing, which has been identified as the main mechanism causing beam degradation in this regime. The challenges in further progressing with the understanding, the modelling and the mitigation of these space charge effects and the resulting beam degradation are discussed. Furthermore, an outlook for possible future directions of studies is presented.