The dissociation and ionization of molecular ions and neutral atoms by the Lorentz force provides a mechanism for trapping energetic particles inside fusion machines without need for ionizing collisions on background gas molecules or arc discharges. At ion energies of interest in fusion work, magnetic dissociation is equivalent to electrostatic dissociation where the equivalent field is E = vB. The range of parameters of interest in thermonuclear research corresponds to effective electric fields up to the order 106 V/cm. The threshold fields for dissociating the successive vibrational levels of all isotopic mixtures of the hydrogen molecular ion, H2+, HD+, HT+, D2+, DT+, T2+, are reported. For the uppermost levels of these (nonrotating) ions the threshold fields range from 0.6 × 105 to 0.9 × 105 V/cm. Rotational effects are discussed in detail. The presence of rotation J introduces J + 1 new thresholds for a particular vibrational level; these thresholds are distributed about the single threshold for the nonrotating ion. The lack of a stepwise dissociation observed in the Riviere-Sweetman experiment can be interpreted as due to a superposition of contributions from rotational states up to J = 4, 5. Methods are discussed for enhancing the populations of the uppermost vibrational levels of the hydrogenic ions. The bound vibrational state belonging to the antibonding electronic state of each of the H2+, D2+, and T2+ ions can be dissociated with fields of the order 104 V/cm; reactions populating these levels are discussed. The formation of neutral hydrogen or deuterium atom beams by the charge exchange reaction provides a population distribution covering all excited states. The equilibrium populations of the excited levels are sufficiently large that the ionization by the Lorentz force competes favorably with the other ionization processes. A 30-keV H atom moving in a 60 kG field is susceptible to ionization down to the n = 8, 9 levels; a 100-keV atom in the n = 6 level is ionized by a 130-kG field. Containment experiments designed on the basis of these data are discussed.