Particle Acceleration in Carbon Nano Tubes

Student: Cristian Bontoiu
Supervisor: Javier Resta Lopez

Particle accelerators have reached the sustainability limit in terms of investment and operation costs versus scientific outcome and large superconducting (SC) machines, such as LHC at CERN, are unlikely to be commissioned in the future. For reaching high energies, conventional SC radio-frequency cavities are invariably used. Accelerating field gradients are typically limited to 30MV/m at the expense of large running costs for microwave and cryogenic power. While research on improved SC material technology has been ongoing for decades [1], there is currently an  increased interest in novel acceleration mechanisms, such as those occurring in plasma [2] and solid-state matter [3]. Both media require 50 - 300 fs laser pulses with wavelength of a few µm for generating wakefields, and the motivation comes from recent proof-of-principle experiments such as those carried out for electron acceleration in laser-plasma interactions [4] and for laser-driven electron lensing in silicon microstructures [5]. So far, the laser-plasma interaction route was favoured due to the ease of generating fresh targets, and significant progress has been achieved. However, there are a number of plasma instabilities which need to be overcome before the proof-of-principle experiments can be turned into a stable multistage accelerator able to deliver bunches with low energy spread. The alternative route of exploiting electric fields generated in solid-state matter has long remained unexplored mainly due to the lack of X-ray laser beams. It has been shown theoretically [6] that TV/m accelerating gradients are possible in a crystal lattice if it is radiated by a laser of 10⁹ W/cm² power density and 5 ps pulse length at Bragg angle, as this stimulates the Bormann anomalous transmission [7]. However, laser beams of such low wavelengths cannot be produced in a controllable manner up to day.

As a hybrid approach between the plasma and solid-state methods, the investigation of high gradient electric fields in carbon nano tubes (CNTs) is proposed through interaction with electron beams and possibly laser pulses. CNTs are single- and multi-walled tubular structures as shown in Figure 1 with a typical diameter of 1.35nm and a C-C bond length of 0.14nm sitting between the solid- and plasma-state in terms of achievable charge density. For instance, with an average CNT mass density of 1.6 g/cm³ the maximum ion density is ~10²² cm^-3, namely 2-3 orders of magnitude higher than plasma densities currently available in supersonic gases. Single-wall CNTs have thermal conduction coeficients of up to 6 kW/(mK) and can sustain current densities of up to 10⁹ A/cm² [8, pp. 215-216]. In addition to their reported tensile strength of ≈45GPa, these features make CNTs a very robust target for interactions with laser and charged-particle beams.

Figure 1: (A) Transmission Electron Microscopy image of a multi-walled CNT in axial cross-section (Berkeley University), and (B) a three-dimensional model (Wikipedia)

The aim is to stimulate charge density ripples along the CNTs by high-frequency electric fields taking benefit of the large axial electrical conductivity. This can be achieved by either irradiating the target with laser pulses or electron bunches. Charge density fluctuations leave the carbon atoms unbalanced electrically and, in consequence, large electric fields are expected to be generated. Their appearance has been already demonstrated when dopped CNTs irradiated by laser pulses of 10 - 20 fs length and 10¹⁷ - 10¹⁸ W/cm² intensity released 1.5MeV protons [9]. A key part of this proposal is the optimization of these electric fields in terms of amplitude and periodicity, such that they can be used for particle acceleration and possibly focusing of a witness particle bunch.

The research and development work is split in two major stages: (1) numerical simulations and (2) proof-of-principle experiment. The first stage requires sophisticated particle-in-cell codes (PIC) such as PIConGPU [10], EPOCH [11] and OSIRIS [12]. As a preliminary milestone, the interaction of electron bunches and laser pulses with two-dimensional charge density ribbons will be studied. Though not completely realistic, due to the low memory and processing power overhead, such a setup enables a quick optimization of the main parameters: wavelength, spot size, length, polarization and power for the laser pulse and energy, emittance, and current for the driving electron bunch. After defining the parameters ranges and boundary conditions, three-dimensional PIC studies will be carried out. This will include modelling the CNTs as granular charge density tubes. Following a refined parametric optimization, acceleration of witness bunches will be attempted numerically. Eventually these simulations will guide the design of a proof-of-principle experiment, depending on  available electron sources and CNTs manufacturers. The experimental work including data acquisition and processing will complete the second stage of this research and development project.

A positive outcome of the project may stimulate further research in solid-state acceleration mechanisms for which a community already exists. It could open the possibility to create small-scale and cost-effective accelerators for fundamental scientific and medical research.

 

References
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