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 $H_{\beta }$ line preliminarily defines the plasma with a free electron density of $(1.9\pm 0.1)\times {10}^{16}{\mathrm{cm}}^{-3}$ and a free electron temperature of 0.8–1.3 eV. The temperature uncertainty results in a wide hydrogen density, ranging from $2.3\times {10}^{16}$ to $7.8\times {10}^{18}{\mathrm{cm}}^{-3}$. A 108 MHz pulsed beam of ${{}^{48}\mathrm{Ca}}^{10+}$ with a velocity of $3.652\mathrm{MeV}/\mathrm{u}$ 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 $(1.9\pm 0.7)\times {10}^{17}{\mathrm{cm}}^{-3}$, and the free electron temperature can be precisely derived as $1.01\pm 0.04\mathrm{eV}$. This method should prove useful in many studies, e.g., inertial confinement fusion or warm dense matter.

Figure 1

The measured $H_{\beta }$ spectrum and a two-peak Lorenz fitting is shown. The measured peak separation of 0.57 nm results in a free electron density of $(1.9\pm 0.1)\times {10}^{16}{\mathrm{cm}}^{-3}$ by using the two-peak separation method [26].

Figure 2

(a) Reference signals and (b) beam signals for vacuum and plasma conditions. Setting both of the minimum peak values of the respective corresponding reference signals as time zero, the beam signals can be directly compared. Applying the deconvoluted beam mass center as a representative, $t_1=3.506\mathrm{ns}$ is obtained for the vacuum condition while $t_2=4.060$ is obtained for the plasma condition. The time difference $\mathrm{\Delta }t$ is obtained as 0.554 ns.

Figure 3

Charge-state distributions of the beam ions. The effective charge state for the pinch plasma target is estimated as $13\pm 1$.