# Anomalous Beam Transport through Gabor (Plasma) Lens Prototype
## 6 Conclusions  
We characterised the operation of an electron plasma (Gabor) lens based on a test at the Surrey Proton Beam Centre with a 1.4 MeV proton beam. Prior measurements at Imperial College indicated that the lens had a stable regime of operation over a range of applied voltage and current. During the beam test, the lens was observed to transform pencil beams into rings. The presence of a plasma was confirmed by matching the measured focusing effect with particle transport calculations. An evaluation of the focusing strength showed that the density of the trapped electrons depends on the strength of the radially confining magnetic field, effects that were well described by simulation. Since the same focusing effects and ring patterns were observed on consecutive days, the plasma instability was associated with the geometry and operation of the lens. The formation of rings indicates that the plasma column is excited into a coherent off-axis rotation. The size of the rings increases with increasing current through the coil. A reproducible modulation of the intensity was observed around the circumference of each ring. The position of the centroids of the rings varied non-linearly with the external magnetic field strength, showing a variable plasma trapping efficiency. The \(x\) and \(y\) diameters, and the eccentricity of the rings were seen to depend on their position with  
Figure 16: The variation in the \(x\) and \(y\) diameter of the six spot data with increasing magnetic field strength. Figure 17: The ratio of the \(x\) diameter to the \(y\) diameter for beam spots in the six spot data with increasing magnetic field strength. respect to the beam axis, as a result of the different \(x\) and \(y\) focusing forces experienced by each pencil beam. Both particle-in-cell and particle-tracking simulations showed that a rotation of the bulk of the plasma transforms pencil beams into rings. The size and width of the rings were shown to be determined by the density of the plasma. Rings with size, eccentricity, and intensity modulation similar to the experimental images were reproduced with a simulation of particle transport through a plasma characterised by the \(m=1\) diocotron instability. The results described here indicate the presence of a mechanism that drives the rotation of the plasma column. Further investigations are required to identify and describe the exact mechanism that needs to be avoided for the lens to be operated as a reliable focusing device. Conceptualization, T.N., T.S.-D., R.B., H.-T.L., K.L., J.P. and C.W. ; data curation, T.N., T.-S.D., C.L.C. and J.P.; formal analysis, T.N., T.-S.D., C.L.C. and J.P.; funding acquisition, K.L. and J.P.; investigation, T.N., T.-S.D., R.B., C.L.C., H.-T.L., K.L., J.P. and C.W. ; methodology, T.N., T.-S.D., K.L. and J.P.; project administration, K.L. and J.P.; resources, K.L. and J.P.; software, T.N., T.-S.D., C.L.C., H.-T.L. and J.P.; supervision, K.L. and J.P.; validation, T.N., T.-S.D. and J.P.; visualization, T.N., T.-S.D. and C.L.C. ; writing--original draft, T.N., T.-S.D., K.L. and J.P.; writing--review & editing, T.N., T.-S.D., R.B., H.-T.L., K.L. and C.W. All authors have read and agreed to the published version of the manuscript. This research was funded by the STFC through the Imperial Impact Acceleration Account. Not applicable. The data presented in this study are openly available in FigShare at [10.6084/m9.figshare.14566485]. We wish to acknowledge the work of [PERSON] at the 2017 beam test. We would also like to the thank all the staff at the University of Surrey Ion Beam Facility, and in particular [PERSON], for his support throughout both days of the beam test. We gratefully acknowledge the Plasma Physics Group at Imperial College London who were generous in sharing their scientific insight and provided technical support at various stages of the project. The work was financially supported by the STFC through the Imperial Impact Acceleration Account. One of us ([PERSON]) gratefully acknowledges the support from the Class of 1964 Scholarship.