# Anomalous Beam Transport through Gabor (Plasma) Lens Prototype
## 1 Introduction  
One of the principal challenges that must be addressed to deliver high-flux pulsed proton or positive-ion beams for many applications is the efficient capture of the ions ejected from the source. A typical source produces protons with kinetic energies of approximately 60 keV [1; 2; 3] and ions with kinetic energies typically below 120 keV [4; 5]. At this low energy the mutual repulsion of the ions causes the beam to diverge rapidly. Capturing a large fraction of this divergent flux therefore requires a focusing element of short focal length. Proton- and ion-capture systems in use today employ magnetic, electrostatic, or radio frequency quadrupoles, or solenoid magnets to capture and focus the beam [2; 6; 7; 8]. Laser-driven proton and ion sources are disruptive technologies that offer enormous potential to serve future high-flux, pulsed beam facilities [9; 10; 11; 12; 13; 14; 15; 16]. Possible applications include proton- and ion-beam production for research, particle-beam therapy, radio-nuclide production, and ion implantation. Recent measurements have demonstrated the laser-driven production of large ion fluxes at kinetic energies in excess of 10 MeV [17; 18; 19; 20]. The further development of present technologies and the introduction of novel techniques [21; 22] makes it conceivable that significantly higher ion energies will be produced in the future [13; 23; 24]. By capturing the laser-driven ions at energies two orders of magnitude greater than those pertaining to conventional sources, it will be possible to evade the current space-charge limit on the instantaneous proton and ion flux that can be delivered. While in some situations the high divergence of laser-driven ion beams can be reduced [25; 26], for the tape-drive targets proposed for medical beams [16; 20] it necessary to capture the beam using a strong-focusing element as close to the ion-production point as possible. An attractive approach to providing the strong-focusing element required to capture the low-energy (\(\sim\)15 MeV) ion flux produced in the laser-target interaction is to exploit the strong focusing forces that can be provided by a cloud of electrons trapped within a cylindrical volume by crossed electric and magnetic fields. Such an electron-plasma lens was initially proposed by [PERSON] in 1947 [PERSON] (1947). The use of electron-plasma lenses of the Gabor type to capture and focus proton and ion beams has been studied by a number of authors [PERSON] (1947); [PERSON] (1947); [PERSON] (1948); [PERSON] (1949); [PERSON] (1950); [PERSON] (1951); [PERSON] (1952); [PERSON] (1953); [PERSON] (1954). Such a lens has the potential to decrease the magnetic field required in the first focusing element by a factor of more than 40 compared with that required for a conventional beam-capture solenoid of the same focusing strength [PERSON] (1953). Consider, for example, a 25 MeV proton beam. A magnetic field strength of 0.06 T is required to achieve a focal length of 1 m using a Gabor lens with an anode length of 0.3 m. To achieve the same focal length using a solenoid requires a field of 2.6 T. Such strong focusing is particularly important when beams are produced with a large divergence angle [PERSON] (1953). The Gabor lens is therefore the ideal focusing element by which to capture a laser-accelerated proton or ion beam. Its compactness and relatively low price are key if it is to be exploited in particle-beam therapy facilities. Furthermore, it has been shown in simulation that a Gabor-lens-based system is capable of capturing laser-generated proton beams at energies as high as 250 MeV, the energy required to serve a proton-beam therapy facility [PERSON] (1953). Following the initial proposal by [PERSON], several groups have reported stable operation of a space-charge lens under a variety of electrode and magnetic field configurations [PERSON] (1947); [PERSON] (1947); [PERSON] (1947); [PERSON] (1947).