Mercury-free metal halide lamp

A mercury-free metal halide lamp comprising:

• an arc tube including a pair of electrodes inside the tube, wherein
• in the arc tube, a rare gas and a metal halide are contained, and no mercury is contained, and
• the mercury-free metal halide lamp is horizontally operated such that the pair of electrodes is substantially horizontal,
• the mercury-free metal halide lamp further comprising magnetic field applying means for applying, in a substantially vertical direction, a magnetic field including a component substantially perpendicular to a straight line connecting heads of the pair of electrodes, wherein
• a density of halogen atoms evaporated during steady-state operation with respect to unit inner volume of the arc tube is 20 μmol/cc or more,
• the lamp satisfies the relationship of Equation, 0<(10BW/f)−Pd<10
• where B(mT) is the magnetic field applied to a center between the heads of the pair of electrodes when the lamp is operated horizontally such that a straight line connecting the heads of the pair of electrodes is substantially horizontal, d(mm) is the distance between the heads of the pair of electrodes, W(W) is the power consumed during steady-state operation, and f(Hz) is the steady-state frequency during steady-state operation, P(MPa) is the pressure of an enclosed rare gas at 20° C.