Effects of target plasma electron-electron collisions on correlated motion of fragmented ${{\mathrm{H}}_2}^{+}$ protons

The objective of the present work is to examined the effects of plasma target electron-electron collisions on ${{\mathrm{H}}_2}^{+}$ protons traversing it. Specifically, the target is deuterium in a plasma state with temperature $T_e=10\mathrm{eV}$ and density $n={10}^{23}{\mathrm{cm}}^{-3}$, and proton velocities are $v_p=v_{\mathrm{th}}$, $v_p=2v_{\mathrm{th}}$, and $v_p=3v_{\mathrm{th}}$, where $v_{\mathrm{th}}$ is the electron thermal velocity of the target plasma. Proton interactions with plasma electrons are treated by means of the dielectric formalism. The interactions among close protons through plasma electronic medium are called vicinage forces. It is checked that these forces always screen the Coulomb explosions of the two fragmented protons from the same ${{\mathrm{H}}_2}^{+}$ ion decreasing their relative distance. They also align the interproton vector along the motion direction, and increase the energy loss of the two protons at early dwell times while for longer times the energy loss tends to the value of two isolated protons. Nevertheless, vicinage forces and effects are modified by the target electron collisions. These collisions enhance the calculated self-stopping and vicinage forces over the collisionless results. Regarding proton correlated motion, when these collisions are included, the interproton vector along the motion direction overaligns at slower proton velocities $(v_p=v_{\mathrm{th}})$ and misaligns for faster ones $(v_p=2v_{\mathrm{th}}$, $v_p=3v_{\mathrm{th}})$. They also contribute to a great extend to increase the energy loss of the fragmented ${{\mathrm{H}}_2}^{+}$ ion. This later effect is more significant in reducing projectile velocity.

Figure 1

(Color online) Drude, RTA, and Mermin energy loss functions dependence with $\omega ∕{\omega }_p$ when $k\to 0$, for a $T_e=10\mathrm{eV}$ and $n={10}^{23}{\mathrm{cm}}^{-3}$ deuterium plasma. The collision frequency is $\nu =0.225{\omega }_p$.

Figure 2

(Color online) $F_z(z,\sigma )$ as a function of $z$ at $\sigma =0$ that a proton $Z_1=1$ with velocity $v=2.5v_{\mathrm{th}}$ produces on another proton located at $(z,\sigma =0)$. RPA case is compared with the RTA and Mermin cases when $\nu =0.225{\omega }_p$.

Figure 3

(Color online) RPA self-stopping ion force as a function of ion velocity in a $T_e=10\mathrm{eV}$ and $n={10}^{23}{\mathrm{cm}}^{-3}$ plasma compared with the Bethe formula. Self-stopping RTA and Mermin forces are compared with the RPA case using collision frequency $\nu =0.225{\omega }_p$.

Figure 4

(Color online) Evolution of the adimensional interproton distance $r{k}_D$ as a function of the logarithm of dwell time $\tau$ during the Coulomb explosion of a ${{\mathrm{H}}_2}^{+}$ ion with the initial angle ${\alpha }_0=60°$ traversing the plasma with different velocities (a) $v_p=v_{\mathrm{th}}$, (b) $v_p=2v_{\mathrm{th}}$, and (c) $v_p=3v_{\mathrm{th}}$. Each graph represents this evolution taking into account only bare Coulomb force, Coulomb and vicinage forces, and Coulomb force and vicinage forces considering target electron collisions.

Figure 5

(Color online) Evolution of $\alpha$ as a function of the logarithm of dwell time $\tau$ when the initial azimuthal angle is ${\alpha }_0=60°$; for the same conditions as in Fig. 4.

Figure 6

(Color online) ${{\mathrm{H}}_2}^{+}$ electronic stopping ratio $R_2$ as a function of the logarithm of dwell time $\tau$ when the initial azimuthal angle is ${\alpha }_0=60°$; for the same conditions as in Fig. 4.