Determination of Hydrogen Density by Swift Heavy Ions

A novel method to determine the total hydrogen density and, accordingly, a precise plasma temperature in a lowly ionized hydrogen plasma is described. The key to the method is to analyze the energy loss of swift heavy ions interacting with the respective bound and free electrons of the plasma. A slowly developing and lowly ionized hydrogen theta-pinch plasma is prepared. A Boltzmann plot of the hydrogen Balmer series and the Stark broadening of the Hβ line preliminarily defines the plasma with a free electron density of (1.9±0.1)×1016 cm-3 and a free electron temperature of 0.8-1.3 eV. The temperature uncertainty results in a wide hydrogen density, ranging from 2.3×1016 to 7.8×1018 cm-3. A 108 MHz pulsed beam of Ca4810+ with a velocity of 3.652 MeV/u is used as a probe to measure the total energy loss of the beam ions. Subtracting the calculated energy loss due to free electrons, the energy loss due to bound electrons is obtained, which linearly depends on the bound electron density. The total hydrogen density is thus determined as (1.9±0.7)×1017 cm-3, and the free electron temperature can be precisely derived as 1.01±0.04 eV. This method should prove useful in many studies, e.g., inertial confinement fusion or warm dense matter.