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IntroductionControlling the transport of large (multi-mega-Ampere) currents of fast electrons in dense plasma is important for the many applications of high power laser-solid interactions, including ion acceleration [1, 2] and radiation production [3,4]. It is also important for the development of the fast ignition (FI) approach to inertial coninement fusion (ICF) [5] in which fast electrons are used to transfer energy from an 'ignition' laser pulse to the compressed Deuterium-Tritium (D-T) fusion fuel. In this scheme, an electron current of the order of giga-Amperes is required to propagate over a distance of 100-200 µm from its source to ignite the compressed fuel. In FI schemes involving a hollow cone (to enable propagation of the ignition laser pulse closer to the compressed fuel) the electrons also propagate through the end wall of the solid-density cone, which is typically 100 µm from the centre of the fuel [6]. The mean electron energy is bound by the requirements for it to be high enough such that the electrons are not subject to extensive scattering losses and low enough that eficient energy deposition occurs in the hot spot. This in turns sets the peak intensity of the ignition laser pulse to the 10 20 Wcm −2 range, as determined by ponderomotive scaling [7]. The energy of the ignition laser pulse depends not only on the ignition physics, but also on the laser-to-electron energy conversion eficiency and the fast electron transport physics. Reduction of the divergence of the electron beam and the minimisation of transport instabilities leading to energy losses (via Ohmic heating) is important to lower the energy requirements of the ignition laser pulse. The development of radically different beam transport patterns, such as 'annular' beams, can also help to achi...