Charge-state distribution measurements of ${}^{238}\mathrm{U}$ and ${}^{136}\mathrm{Xe}$ at $11\mathrm{MeV}/\mathrm{nucleon}$ using gas charge stripper

The charge-state distributions and equilibrium charge states of uranium (${}^{238}\mathrm{U}$) and xenon (${}^{136}\mathrm{Xe}$) ions at $11\mathrm{MeV}/\mathrm{nucleon}$ were determined using a gas charge stripper. A differential pumping system facilitated the increase of the nitrogen gas thickness up to $1.3\mathrm{mg}/{\mathrm{cm}}^2$, which is sufficient for the most probable charge state to attain equilibrium. The charge states of ${}^{238}\mathrm{U}$ attain equilibrium at 56.0, 56.6, and 55.7 in ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ media with thicknesses of 125, 79, and $126\mu \mathrm{g}/{\mathrm{cm}}^2$, respectively, while those of ${}^{136}\mathrm{Xe}$ attain equilibrium at 40.5, 40.1, and 40.3 in ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ media with thicknesses of 163, 95, and $139\mu \mathrm{g}/{\mathrm{cm}}^2$, respectively. The equilibrium charge states of ${}^{136}\mathrm{Xe}$ are acceptable for acceleration by the subsequent cyclotron. The measured data of ${}^{238}\mathrm{U}$ were used to devise an empirical formula for the prediction of the equilibrium charge state in gaseous media over the energy region of $0.01–60\mathrm{MeV}/\mathrm{nucleon}$. The equilibrium charge state of ${}^{136}\mathrm{Xe}$ as predicted by the devised formula is in good agreement with the data.

Figure 1

Acceleration scheme at RIBF. The ${}^{238}\mathrm{U}$ or ${}^{136}\mathrm{Xe}$ beams are accelerated by means of a linear accelerator and four cyclotrons. A pair of charge stripper sections is located downstream of the first and second cyclotrons, the RRC and the fRC, respectively.

Figure 2

The data of equilibrium charge state for uranium ions in (a) solid and (b) gaseous media. (a) Open circles represent data for solid materials [4, 11, 12, 13, 14, 15, 16, 17]. Dashed, dotted, and dash-dotted curves represent the charge states for solid materials as predicted by the empirical formulas proposed by Leon [15], Baron [18], and Schiwietz [19], respectively. In the energy region of $40–1000\mathrm{MeV}/\mathrm{nucleon}$, the simulation results of GLOBAL [35] for carbon are represented by open triangles. The shaded area indicates the deviation of predicted values. (b) Solid circles represent data for gases [11, 12, 16, 17]. Orange, green, blue, cyan, and magenta curves represent the charge states for gases as predicted by the empirical formulas proposed by Betz [28], Strehl [31], Sayer [30], Betz [29], and Schiwietz [19], respectively. The simulation results of GLOBAL for nitrogen are represented by solid triangles. The shaded area indicates the deviation of predicted values.

Figure 3

Schematic diagram of the gas charge stripper with its differential pumping system [32]. Gases are injected in the target cell (stage 1) located at the center. The length of the target cell is 14 cm. Other stages are also shown along with the pumping speeds of their respective attached pumps. The beam passes through four apertures (6 mm in diameter) to enter the target cell. The exits of the target cell and stage 2 are also 6-mm-diameter apertures. The exits of stage 3 and 4 are 8 and 10 mm diameter apertures, respectively.

Figure 4

Overview of the gas charge stripper system for the offline test. The gas charge stripper chamber and two mechanical booster pumps (MBP1 and MBP2) are shown in the photograph.

Figure 5

The pressure at each stage (${\mathrm{P}}_2–{\mathrm{P}}_5$) is plotted as a function of ${\mathrm{P}}_1$. Stage 5 has two separated areas, stage 5-1 and stage 5-2, which correspond to the areas upstream and downstream of stage 4, respectively. The pressures at stages 5-1 and 5-2 are denoted by ${\mathrm{P}}_{5\mathrm{\text{−}}1}$ (blue) and ${\mathrm{P}}_{5\mathrm{\text{−}}2}$ (green), respectively. The solid line indicates the limit for an interlock ($4\times {10}^{-3}\mathrm{Pa}$). The pressures at stages 6-1 and 6-2 are denoted by “beamline1” and “beamline2” and are maintained lower than the interlock limit if ${\mathrm{P}}_1$ is lower than 7.7 kPa.

Figure 6

(a) Energy spectra of alpha particles after passing through the gas cell filled with ${\mathrm{N}}_2$ gas at different pressures ${\mathrm{P}}_1$. The spectrum in the case of no gas injection is represented by solid circles. Asterisks, open circles, open triangles, open squares, and open diamonds represent the spectra with ${\mathrm{P}}_1$ at 0.25, 0.52, 0.92, 2.02, and 4.58 kPa, respectively. (b) Gas thickness estimated from the energy loss measurement is plotted as a function of ${\mathrm{P}}_1$. The data for ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ gas injections are represented by solid circles, solid triangles, and solid squares, respectively. Fitting functions are represented by solid curves of cyan, red, and green for ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ gas injections, respectively.

Figure 7

The beam line from the RRC to the fRC. The gas charge stripper is located upstream of the fRC.

Figure 8

Schematic view of the gas charge stripper. The beam intensity upstream of the gas charge stripper was measured using a Faraday cup (FC-D16). Stripped beams were analyzed using a pair of dipole magnets DAD4 and DMD4. The beam intensity downstream of DAD4 and DMD4 was measured using a Faraday cup (FC-F41).

Figure 9

Charge-state distributions of ${}^{238}\mathrm{U}$. The data of fractions calculated for (a) ${\mathrm{N}}_2$, (b) Ar, and (c) ${\mathrm{CO}}_2$ are plotted. (a) The data for the ${\mathrm{N}}_2$ gas medium with thicknesses of 48, 84, 150, 334, and $752\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by asterisks, open triangles, open circles, open squares, and open diamonds, respectively. (b) The data for the Ar gas medium with thicknesses of 39, 106, 205, and $474\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by open triangles, open circles, open squares, and open diamonds, respectively. (c) The data for the ${\mathrm{CO}}_2$ gas medium with thicknesses of 32, 61, 122, 225, and $516\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by asterisks, open triangles, open circles, open squares, and open diamonds, respectively.

Figure 10

The most probable charge states of ${}^{238}\mathrm{U}$ are plotted as a function of gas thickness. The data for ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ are represented by solid circles, solid triangles, and solid squares, respectively. Fitting functions are represented by solid curves. The error in thickness is because of the uncertainty of the fitting parameter obtained in Sec. 2c and the fluctuation of pressure ${\mathrm{P}}_1$ during the measurement.

Figure 11

Charge-state distributions of ${}^{136}\mathrm{Xe}$. The data of fractions calculated for (a) ${\mathrm{N}}_2$, (b) Ar, and (c) ${\mathrm{CO}}_2$ are plotted. (a) The data for the ${\mathrm{N}}_2$ gas medium with thicknesses of 47, 85, 150, 336, and $752\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by asterisks, open triangles, open circles, open squares, and open diamonds, respectively. (b) The data for the Ar gas medium with thicknesses of 27, 94, 196, and $462\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by open triangles, open circles, open squares, and open diamonds, respectively. (c) The data for the ${\mathrm{CO}}_2$ gas medium with thicknesses of 5, 11, 50, 111, 217, and $506\mu \mathrm{g}/{\mathrm{cm}}^2$ are represented by crosses, asterisks, open triangles, open circles, open squares, and open diamonds, respectively. Solid lines are curves fitted using Gaussian functions.

Figure 12

Most probable charge states of ${}^{136}\mathrm{Xe}$ are plotted as a function of gas thickness. The data for ${\mathrm{N}}_2$, Ar, and ${\mathrm{CO}}_2$ are represented by solid circles, solid triangles, and solid squares, respectively. Fitting functions are represented by solid curves. The error in thickness is because of the uncertainty of fitting parameter obtained in Sec. 2c and the fluctuation of the pressure ${\mathrm{P}}_1$ during the measurement.

Figure 13

The data obtained at RIKEN are plotted by solid squares along with other available data for gases [11, 12, 16, 17] shown in Fig. 2. The new fitting function $q_{\mathrm{eq}}=Z[1-1.01\exp \{-(v/v_0{)}^{0.990}{Z}^{-0.676}\}]$ is also indicated by a solid curve.

Figure 14

The equilibrium charge states for xenon in gaseous media as predicted by the new fitting function is indicated by a solid curve. The data obtained from Refs. 12, 36 are indicated by solid circles. The data obtained in this work is indicated by solid squares.