Theoretical investigations show that linearly and radially polarized multiterawatt and petawatt laser beams, focused to subwavelength waist radii, can directly accelerate protons and carbon nuclei, over micron-size distances, to the energies required for hadron cancer therapy. Ions accelerated by radially polarized lasers have generally a more favorable energy spread than those accelerated by linearly polarized lasers of the same intensity.PACS numbers: 52.28. Kd, 37.10.Vz, 52.75.Di Protons and heavier ions are now being used to treat cancer at a number of places around the world [1]. Ion lithography schemes seem to be heading for practical application [2] and fusion research continues to attract considerable attention and to gain in importance [3]. In addition, considerable effort is being devoted to research into the fundamental forces of nature, the initiation of nuclear reactions and into schemes to treat radioactive waste [4]. In these applications, conventional accelerators (synchrotrons, cyclotrons and linacs) are employed which are large and expensive to build and operate.To produce and accelerate ions, current plasma-based research focuses on the use of thin foils irradiated by femtosecond laser pulses of intensity > 10 18 W/cm 2 [5]. Typically a laser pulse is incident on the thin foil giving rise to an overdense plasma from which the electrons get accelerated, form a dense sheath on the opposite side and generate a quasistatic electric field of strength in excess of 10 12 V/m. This superstrong field accelerates the ions to tens of MeV over a distance in the µm range [6]. Recent work [7] has shown that proton beams produced by this method of target normal sheath acceleration (TNSA) may be improved in energy and beam quality by the use of foils less than 1 µm in thickness [8]. In earlier experiments, employing thicker foils, a small fraction of the energy got converted to proton energy. Furthermore, the protons had energy spreads reaching 100%.In hadron therapy [9, 10,11], for example, the ions are required to have kinetic energies K = 20 − 250 MeV/nucleon (H + and He 2+ ) and K = 85 − 430 MeV/nucleon (C 6+ and O 8+ ). The ions also ought to have an energy spread ∆K f /K f < 1% so that they may be focused on the tumor while sparing the neighboring healthy tissue. A beam of rectangular cross section is also desirable [11].In this Letter we study direct laser acceleration configurations of protons and bare carbon nuclei. The aim is to make predictions regarding the optimum conditions that would lead to the ion energies of interest to hadron therapy. A source for the ions may be a dedicated electron beam ion trap/source (EBIT/EBIS) [12] from which they can be extracted in a well-defined fully ionized charge state or an ensemble of fully stripped ions produced by laser-solid interaction. We consider a situation in which the source has been tailored on a nanoscale [9,13]. We study the dynamics of an ensemble of N particles having normally distributed kinetic energies, using the singleparticle relativistic...