Cancer is the second most common cause of death globally, accounting for 8.8 million deaths in 2015. It is estimated that radiotherapy is used in the treatment of approximately half of all cancer patients. In the UK, one new NHS proton-beam therapy facility has recently come online in Manchester and a second will soon be brought into operation in London. In addition, several new private proton-beam therapy facilities are being developed. The use of these new centres, and the research that will be carried out to enhance the efficacy of the treatments they deliver, will substantially increase demand. Worldwide interest in particle-beam therapy (PBT) is growing and a significant growth in demand in this technology is anticipated. By 2035, 26.9 million life-years in low- and middle-income countries could be saved if radiotherapy capacity could be scaled up. The investment required for this expansion will generate substantial economic gains. Radiotherapy delivered using X-ray beams or radioactive sources is an established form of treatment widely exploited to treat cancer. Modern X-ray therapy machines allow the dose to be concentrated over the tumour volume. X-ray dose falls exponentially with depth so that the location of primary tumours in relation to heart, lungs, oesophagus and spine limits dose intensity in a significant proportion of cases. The proximity of healthy organs to important primary cancer sites implies a fundamental limit on the photon-dose intensities that may be delivered. Proton and ion beams lose the bulk of their energy as they come to rest. The energy-loss distribution therefore has a pronounced 'Bragg peak' at the maximum range. Proton and ion beams overcome the fundamental limitation of X-ray therapy because, in comparison to photons, there is little (ions) or no (protons) dose deposited beyond the distal tumour edge. This saves a factor of 2-3 in integrated patient dose. In addition, as the Bragg peak occurs at the maximum range of the beam, treatment can be conformed to the tumour volume. Protons with energies between 10MeV and 250MeV can be delivered using cyclotrons which can be obtained `off the shelf' from a number of suppliers. Today, cyclotrons are most commonly used for proton-beam therapy. Such machines are not able to deliver multiple ion species over the range of energies required for treatment. Synchrotrons are the second most common type of accelerator used for proton- and ion-beam therapy and are more flexible than cyclotrons in the range of beam energy that can be delivered. However, the footprint, complexity and maintenance requirements are all larger for synchrotrons than for cyclotrons, which increases the necessary investment and the running costs. We propose to lay the technological foundations for the development of an automated, adaptive system required to deliver personalised proton- and ion-beam therapy by implementing a novel laser-driven hybrid accelerator system dedicated to the study of radiobiology. Over the two years of this programme we will: * Deliver an outline CDR for the 'Laser-hybrid Accelerator for Radiobiological Applications', LhARA; * Establish a test-bed for advanced technologies for radiobiology and clinical radiotherapy at the Clatterbridge Cancer Centre; and * Create a broad, multi-disciplinary UK coalition, working within the international Biophysics Collaboration to place the UK in pole position to contribute to, and to benefit from, this exciting new biomedical science-and-innovation initiative.