A new accelerator concept with the potential to reach order of magnitude larger particle energies is proposed. In the concept a large cylindrical cloud of charged particles is radially injected and compressed inside a long solenoid by a rising magnetic field. The cloud is permitted to expand axially and as a result, the particles positioned near the head of it attain very large energies. If the compressing magnetic field rises to ~ 105 G in about ~ 10-5 sec, and if the solenoid is ~ 10 km long, the attainable particle energies are ~ 1013 eV, and if two expanding clouds collide the equivalent stationary target energies for electrons are as large as ~ 1020 eV and for protons ~ 1017 eV. Using megagauss magnetic flux compression techniques the attainable particle energies can reach ~ 1014 eV, with equivalent colliding beam energies of ~ 1022 eV for electrons and 1019 eV for protons.