Stability of the HOPG target

The HOPG target composes with a number of graphene layers. After the beam bombardment, the graphene layers on the surface were damaged and formed flakiness and wrinkles structure as depicted in Fig. \ref{hopg}. This radiation damage modifies the surface structure and may potentially influence the detection of low-energy charged particles, a phenomenon that has not yet been studied. We studied the influence of intense beam irradiation on the HOPG target by measuring $^{12}$C+$^{12}$C reaction yields. In the test, the $^{12}$C$^{2+}$ beam at a relatively high energy of $E_{\rm c.m.}$= \SI{3.55}{MeV} was chosen in order to have a sufficient statistics within a few minutes. The detector was placed at the angle of \SI{120}{\degree} with a gas pressure of 99 mbar. During the charge accumulation, the beam is $^{12}$C$^{2+}$ with a typical current of 40 $\sim$ \SI{50}{p\micro A}. Two kinds of targets, \SI{4}{-\micro m} thick DLC (Diamond-Like Carbon)~\cite{Khalaj2013} and \SI{2}{-mm} thick HOPG targets~\cite{Zhong2023}, were used to study the variations in the yields of carbon carbon fusion reaction as a function of beam dose.An infrared camera was employed to monitor the maximum temperature of the targets. Observations indicated that the beam spot size on DLC and HOPG was approximately \SI{1}{cm^2}. With the water cooling at the back of the target, the maximum temperature of the surface of DLC was stabilized around \SI{100}{\celsius}. However, the surface temperature of the HOPG target quickly rises to $\sim$\SI{400}{\celsius} when the beam hits it. This difference might be caused by the weak interlayer interactions between individual graphene layers in the HOPG target~\cite{Zhou2021,Zhong2023}. Such a structure leads to low through-plane thermal conductivity which is more than two orders of magnitude lower than that of natural graphite. The formation of flakiness and wrinkle structure after irradiation further reduces the thermal conduction. During the measurement, the TPC was placed at \ang{120}. The detector chamber was filled with a mixture gas consisting of 90\% He, 5\% CO$_{2}$, and 5\% Ar at a pressure of \SI{100}{mbar}. As discussed in the section above, the alpha yield is determined directly by selecting the alpha band in the $D E{\rm_{TPC}}-E{\rm_{si}}$ condition and the track information. For protons, they can be selected by applying the anti-alpha condition which excludes the alpha events in the $D E{\rm_{TPC}}-E{\rm_{si}}$ spectrum. The reaction Q values for proton (Q$_{g.s.}$= \SI{2.24}{MeV}) and alpha (Q$_{g.s.}$= \SI{4.62}{MeV}) channels are calculated according to the following formula:\begin{equation}Q = \left(\frac{A_{a}}{A_{B}}-1\right)E_{a} + \left(\frac{A_{b}}{A_{B}}+1\right)E_{b} - \frac{2\sqrt{A_{a}A_{b}E_{a}E_{b}} \cos \theta}{A_{b}}\end{equation}where $A_{a}$, $A_{b}$ and $A_{B}$ are the mass number of the projectile, ejectile and the residual nucleus. $E_{a}$ is the kinetic energies of projectile at reaction and $E_{b}$ is the energy of ejected light particles; $\theta$ is the scattering angle of particle $b$. $E_{b}$ was obtained with the energy detected by the silicon detector and the energy losses in the entrance window and gas region~\cite{ShaoboMa2019}.To reduce the systematic error arising from the energy loss correction, only the events measured by two silicon detectors in the middle are used. The Q-value spectra for $^{12}$C($^{12}$C,$\alpha$)$^{20}$Ne and $^{12}$C($^{12}$C,$p$)$^{23}$Na at $E\rm_{c.m.}$= \SI{3.55}{MeV} are displayed as Fig. \ref{Qspe_3.55_a} and \ref{Qspe_3.55_p}, respectively. The green line in Fig. \ref{Qspe_3.55_a} shows the Q-value spectrum for $^{12}$C($^{12}$C,$\alpha$)$^{20}$Ne using the DLC target at beam charge of 2.18$\times 10^{4}$ $\mu C$. This spectrum was measured at the beginning of beam irradiation. The $\alpha_0$ and $\alpha_1$ peaks are located at Q values of \SI{4.62}{MeV} and \SI{2.99}{MeV}, respectively. There is no noticeable change in the Q-value spectrum during the subsequent charge accumulation on DLC. The black and blue lines in Fig. \ref{Qspe_3.55_a} are obtained for the HOPG target with the accumulated charges of \SI{4.82e4}{\micro\coulomb} and \SI{4.94e6}{\micro\coulomb}, respectively. Comparing the shape of Q-value spectra of HOPG and DLC targets, we can observe clearly a shift and broadening in $\alpha_0$ and $\alpha_1$ peaks for HOPG as beam dose increases. Similarly, the black and blue lines in Fig. \ref{Qspe_3.55_p} represent the Q value spectra for protons corresponding to \SI{2.59e5}{\micro\coulomb} and \SI{4.94e6}{\micro\coulomb} on HOPG, respectively. $p_0$ and $p_1$ peaks locate at Q values of \SI{2.24}{MeV} and \SI{1.80}{MeV}, respectively. The $p_0$ and $p_1$ peaks become broader and developed a longer tail towards the lower Q-value region after the radiation of about \SI{5}{\coulomb}. We investigate the dependence of the measured alpha and proton yields on the beam dose. The reaction yields are calculated by integrating the peaks of proton and alpha in Q-value spectra divided by the incident beam particles. The yield variations of $\alpha_{0}$ and $p_{0} + p_{1}$ are shown in Fig. \ref{yield_3.55_HOPG_a_acc_charge_exp} and \ref{yield_3.55_HOPG_p01_acc_charge}, respectively, as a function of accumulated charge. For each channel, three different yields corresponding to different integral ranges in the Q-value spectra (indicated by the red lines in Fig. \ref{Qspe_3.55_a} and \ref{Qspe_3.55_p}) are obtained to account for the change in the Q-value spectra. It is observed that with an increase in charge on HOPG, both the yields of $\alpha_{0}$ and $p_{0} + p_{1}$ exhibit a notable decrease. This situation becomes more serious for the alpha emission channel. The decreasing trend in the yield of $\alpha_{0}$ (\SI{4.0}{MeV} \textless Q-value \textless \SI{5.0}{MeV})for HOPG can be well-fitted by the following exponential function:\begin{equation}\text{Yield(/$^{12}$C)} = \exp(-26.68-1.47 \times 10^{-7} \times \text{charge/$\mu C$})\end{equation}According to the fitted yield curve shown in Fig. \ref{yield_3.55_HOPG_a_acc_charge_exp}, the yield of $\alpha_{0}$ decreases by 34.9\% when the dose reach \SI{3.0e6}{\micro\coulomb} and by 51.5\% when the dose reaches \SI{5.0e6}{\micro\coulomb}. To mitigate the broadening effect induced by beam irradiation, we employed two extended integral ranges, specifically [\SI{3.5}{MeV}, \SI{5.0}{MeV}] and [\SI{3.1}{MeV}, \SI{5.0}{MeV}]. Compared to the integration within [\SI{4.0}{MeV}, \SI{5.0}{MeV}], the alpha yields increase by 22.0(0.8)\% and 28(1)\% respectively when the dose reaches \SI{4.94e6}{\micro\coulomb}. The $\alpha_{0}$ yield obtained from the three different integral ranges exhibit a similar trend as the accumulated charge increases from \SI{0}{\coulomb} to $\sim$\SI{5}{\coulomb}. As a comparison, we did the same test with the DLC target. The maximum beam dose reaches \SI{5.5e6}{\micro\coulomb}. The yield of $\alpha_{0}$ is approximately constant at 2.70$\times 10^{-12}$ /$^{12}$C according to the fitted yield line as shown in Fig. \ref{yield_3.55_HOPG_a_acc_charge_exp}.  The DLC target contains some fraction of Hydrogen. The yield difference for DLC and HOPG targets at nearly zero dose can be explained by the difference of stopping power. Regarding the $p_{0}$+$p_{1}$ yield, the situation becomes slightly different.When the beam charge is accumulated upto \SI{5.0e6}{\micro\coulomb}, the yield decrease by 25\% according to the fitted yield curve shown in Fig. \ref{yield_3.55_HOPG_p01_acc_charge}. The decrease of the $p_{0} + p_{1}$ yield can be reduced to 7.0(0.3)\% if the integration range is enlarged to [\SI{0.3}{MeV}, \SI{2.4}{MeV}].