Beam diameter effects on the transmission of 1-MeV protons through an insulating macrocapillary
Introduction
After the first observation of ion guiding through insulating nanocapillaries in 2002 [1], the interactions of ions with insulating nano- and macrocapillaries have received considerable attention [2], [3], [4]. The guiding phenomena are attributed to the charge patches formed in a self-organizing manner [1], [5], [6], which produce the electrostatic repulsion that is capable to inhibit close collisions of subsequent ions with the capillary atoms and, in turn, charge exchange. Consequently, the ions are guided through the capillary with their initial energy and charge state, even when the capillary is tilted by large angles with respect to the incident beam direction. Various theoretical simulations [7], [8], [9], [10] demonstrate that the key to the patch formation is the balance between the charge deposition and its depletion governed by the incident current and by the material conductivities, respectively.
To date, experimental and theoretical investigations on transmission of ions in the keV energy region have been extensively performed using different capillary materials [2], [3], [4] (references therein). All the results suggest the dominance of the charge patch deflections in keV-ion guiding. Nevertheless, when the ion energy is increased to several hundred keV [11], [12] and even to one or more MeV [13], [14], [15], [16], [17], the atomic scatterings take over the transmission through insulating capillaries from the patch deflections. This is in agreement with the prediction of the scaling law established by Stolterfoht et al. [18], which indicates that the charge-to-energy ratio of the incident ion is the key parameter for guided transmission.
Due to the increasing interest in mechanisms of MeV ions through insulating macrocapillaries, the ATOMKI group [19], [20] conducted experimental research using a 1-MeV proton microbeam with a diameter of . It was found that the transmitted microbeam suffered little energy loss and exhibited time-dependent evolution. Moreover, the transmitted fraction at equilibrium reached up to . These experimental observations, contrary to previous reports, prove the MeV-ion guiding through the insulating macrocapillary.
Theoretical simulations [21], [22], [23], devoted to microbeam transmission through polytetrafluoroethylene (PTFE) macrocapillaries with relatively small conductivities, provided detailed understanding of MeV-ion guiding. In the series of simulations, a linear charge depletion via the surface or bulk conductivities of the capillary materials was adopted, which is widely used in previous calculations [8], [12], [24] for keV ions through insulating macrocapillaries. The simulated results indicate that the MeV ion guiding is attributed to the ultra extension of charge patch, which results from the beam divergence [23]. A usual proton beam, whose diameter is equal to that of the capillary, was adopted in the recent simulation [25] showing the combined effect of the charge patch deflections and atomic scatterings. In this case, the transmitted fraction was found to be lower than that for microbeam, although they have the same energy and beam current and divergence. This suggests an influence of the beam diameter variation on MeV-ion guiding, which needs detailed interpretation.
In this work we aim to theoretically study the influence of the beam diameter on 1-MeV proton transmission through a straight macrocapillary made of PTFE material. The macrocapillary has a diameter of and a length of . The beam diameter was varied from to , covering more than 2 orders of magnitude. The charge patches formed by the deposited protons and their produced deflection fields within the macrocapillary were discussed. The present simulations show a decreasing transmission of guided protons with increasing the beam diameter. To interpret this beam-diameter effect, an analytic model was established, showing excellent agreement with the simulation results.
Section snippets
Basic considerations of simulations
The simulation methods can be found in our previous work [25] so that only a few details are pointed out here. The energy of the proton beam is fixed to be , whose divergence is full width at half maximum (FWHM). The beam diameter d was varied within the range from to . The beam current is and its density varies accordingly.
The beam enters into a straight macrocapillary with a diameter of and a length of . The charges deposited within the capillary by
Trajectories and charge patch
To obtain visual depictions of the transmission for 1-MeV proton beams, a series of selected trajectories accompanied by deposited charges are presented in Fig. 1. The panels from top to bottom show trajectories obtained with an unchanged tilt angle of and increasing beam diameters.
The transmitted proton trajectories for different beam diameters exhibit a similar behavior that they undergo one deflection and then pass through the capillary, revealing the occurrence of the MeV-ion guiding. It
Analysis and discussion
In the following an analytic model is considered providing insights into the beam diameter effects on the guided transmission of 1-MeV protons. Similar to the treatment introduced by Stolterfoht [27], we propose the schematic diagram depicted in Fig. 4. The blue area represents the guided protons, while the red indicates the protons deposited onto the capillary wall. Based on the geometrical relation indicated at the bottom of Fig. 4, the blue area A is exactly given bywith
Conclusions
We have presented the simulated transmission of 1-MeV protons through a straight PTFE macrocapillary, using different beam diameters. The main attention was paid to how the diameter of the proton beam, differing by more than two orders of magnitudes, affects the guided transmission. The simulation program used here includes two mechanisms that can cause the proton transmission: charge patch deflections and atomic scatterings. The depletion of the charge patch was assumed to follow an
CRediT authorship contribution statement
S.D. Liu: Conceptualization, Methodology, Software, Formal analysis, Writing - original draft, Funding acquisition. Y.T. Zhao: Writing - review & editing, Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work is supported by the special funds for theoretical physics in the National Natural Science Foundation of China (Grant No. 11947051), the Shandong Provincial Natural Science Foundation (Grant No. ZR2018BA035), and by Higher Educational Youth Innovation Science and Technology Program Shandong Province (Grant No. 2020KJJ004).
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