Study on Test‐Mass Charging for Taiji Gravitational Wave Observatory

Taiji is proposed as a space‐based gravitational wave (GW) observatory consisting of three spacecraft in a heliocentric orbit meanwhile with the distance of 3 million kilometers ahead of the Earth at about 20°. Free‐falling test masses (TMs) are a key component of the interferometer for space‐based GW detection in the 0.1mHz–1 Hz frequency range. Exposure to energetic particles in the space environment can lead to charging of the TMs and thus cause additional electrostatic forces and Lorentz forces that limit the sensitivity of the interferometer and may affect the quality of the scientific data. This study aims to model the charging of TMs during Galactic cosmic rays and solar proton events (SPEs) using the Monte Carlo simulation toolkit meanwhile with constructing the sophisticated 3D spacecraft. The results show that the total net charging rates are 34.48 +e/s and 33.85 +e/s on TM1 and TM2 during the solar minimum, and 9.58 +e/s on TM1 and 9.65 +e/s on TM2 during the solar maximum. We confirm that no matter for solar minimum or solar maximum, protons contribute to the largest proportion of the TMs charging rate. Furthermore, charging for five typical SPEs is also investigated, and the maximum TMs charging rate reaches 76,674 +e/s, indicating that sporadic SPEs have a high risk for TMs charging. Finally, the charging rates of a TM imitation are tested on ground by the 30–50 MeV proton irradiation experiment, and the experimental results show good consistence with the simulation results with the error <10%.

In the realm of space-based GW detection, laser interferometers operate on similar principles as their ground-based counterparts, albeit with significantly reduced levels of detection-related noise.Nonetheless, the success of space-based GW detection relies on maintaining test masses (TMs) in free-falling conditions and utilizing baselines spanning millions of kilometers to detect minuscule tidal strains.The space environment poses significant challenges in terms of noise for space-based GW detection, primarily due to high-energy particles, plasma, residual gas, and localized temperature fluctuations.Galactic cosmic rays (GCR) with energies surpassing 100 MeV/n, and the high-energy particles emitted by the Sun, can traverse the outer shielding of spacecraft and reach the TMs, resulting in the generation of pseudo-Coulomb and Lorentz force noise during the charging process.Therefore, it is crucial to forecast the net charging rate and effective charging rate of the TMs before the launch of Taiji.Simulations have been employed to estimate the effects of space plasma (Lu et al., 2021), GCR (Armano et al., 2023;Bao et al., 2007;Grimani et al., 2005;Rui-Long et al., 2021), and solar cosmic rays (Han et al., 2023;Vocca et al., 2005).To limit the intensity of accelerator noise resulting from charge deposition, periodic discharges in orbit are achieved through the application of ultraviolet beam irradiation (Armano et al., 2018;Inchauspé et al., 2020).
Considerable prior works have been undertaken to establish the anticipated charging rates of particles from GCR and solar proton events (SPEs) for LISA and LISA Pathfinder missions (Armano et al., 2023;Grimani et al., 2005;Vocca et al., 2005;Wass et al., 2005).The majority of these investigations relied on simulations performed with the Geant4 Monte Carlo simulation toolkit.A portion of these investigations utilized the Fluka Monte Carlo simulation toolkit (Grimani et al., 2015;Vocca et al., 2004).Notably, when accounting for identical input particle flux and spacecraft geometry, the simulation results from both sets of studies exhibited remarkable consistency.These comprehensive studies revealed positive charging rates in the range of 11-50 +e/s for GCR with respect to LISA and LISA Pathfinder missions (Araújo et al., 2005;Sumner et al., 2004Sumner et al., , 2009)).However, the Taiji mission has had relatively few TM charging studies.This study aims to simulate the charging process of the Taiji mission's TMs using a sophisticated spacecraft geometry model and estimate the associated charging risks.The CREME96 model was adopted as the simulation input for GCR, while data from the GOES satellite's high-energy particle detector served as the input model for SPEs.The charging process of GCR protons, 3 He, and 4 He, and the peak energy spectra of five typical SPEs were simulated using the Geant4 toolkit.Furthermore, the time required for the Taiji TMs to reach the discharge threshold under different environmental conditions was evaluated.Additionally, we validate the charging process of TMs in space-based GW detection by carrying out the ground-based experiments at the 50 MeV proton cyclotron at Huairou, China.The experiment and simulation results are then compared.

Energetic Particle Radiation Environments
The Taiji GW detection spacecraft follows an orbit around the Sun that closely resembles Earth's orbit, making it susceptible to GCR and high-energy solar particle bombardment.As depicted in Figure 1, the positions of the three Taiji spacecraft vary over time along their respective orbits (Z.Luo et al., 2021).These spacecrafts maintain distances from the Sun ranging approximately between 149 and 152 × 10 6 km (0.9933-1.0133 astronomical unit (AU)), with their latitudes relative to the ecliptic plane shifting within 1°.The Ulysses mission conducted a comprehensive investigation of the heliospheric latitudes of the interstellar medium and the solar wind.Notably, Ulysses determined a gradient of about 3% per AU and (0.33 ± 0.04)% per degree for galactic protons with energies exceeding 106 MeV (Heber et al., 1996).This implies that the expected disparities in cosmic rays environmental conditions between Earth and the Taiji spacecraft's vicinity can be considered negligible.However, due to Earth's magnetic field and atmosphere acting as impediments to cosmic rays, we did not adopt the parameterized spectral approach proposed by the LISA team, which utilizes data from balloons and low-orbit satellites (Grimani et al., 2004).Instead, we employ the internationally recognized CREME96 space environment model.Since the influence of Earth on the spectrum of high-energy cosmic particles at geosynchronous satellite orbital positions is essentially negligible, cosmic rays spectrum data at these orbits can be utilized to estimate the charging process of the Taiji spacecraft.

Galactic Cosmic Rays
The intensity of the GCR spectrum varies with the solar cycle, with the highest flux occurring during solar minimum.During solar minimum, the GCR spectrum is predominantly composed of approximately 90% protons, 8% helium nuclei ( 3 He and 4 He), 1% heavy nuclei, and 1% electrons.The external shielding of the Taiji GW detection spacecraft is engineered to withstand impacts from 100 MeV protons; thus, our analysis exclusively considers particles with energies exceeding 100 MeV/n in the charging process of the TMs.The primary nuclei from GCR (protons, 3 He, and 4 He) constitute the fundamental components of our simulation input.
The energy spectra of protons, 3 He, and 4 He at a distance of 1 AU from the Sun during periods of solar maximum and solar minimum were computed using the CREME96 model.Notably, the cosmic ray energy spectrum data obtained from the CREME96 model does not distinguish between 3 He and 4 He, necessitating a parameterization of the cosmic ray He spectrum.Measurement experiments pertaining to the 3 He/ 4 He ratio, designated as C, have yielded relatively precise and comprehensive results (Abe et al., 2014;Casolino et al., 2011;Myers et al., 2003;Wang et al., 2002).Tables 1 and 2 present the values of C(M) for solar maximum and C(m) for solar minimum activity periods (Grimani et al., 2005).
By employing the parameterized 3 He/ 4 He ratio C for solar maximum and solar minimum, as detailed in Tables 1  and 2, we calculate the fluxes of 3 He and 4 He during solar maximum and solar minimum.This computation is accomplished by substituting these values into Equations 1 and 2, which are utilized to ascertain the fluxes of 3 He and 4 He based on the flux of 3+4 He, as determined from the CREME96 model, as illustrated in Figure 2.
(1) ( where C is the ratio of 3 He to 4 He and

Solar Proton Events
SPEs primarily consist of 90% protons, along with alpha particles and heavy ions.These events are closely associated with solar flares and coronal mass ejections, resulting in accelerated particle energies that can reach several GeV.Consequently, SPEs play a pivotal role in influencing the charging of the TMs within the Taiji GW detection system.To comprehensively assess the impact of SPEs on TMs charging, we employ energy spectra derived from data collected by the high-energy proton detector on the GOES satellite (Han et al., 2023).Our analysis focuses on five representative SPEs, and their respective differential energy spectra are depicted in Figure 3.

Taiji Geometry Model
The charging process of the Taiji TMs was simulated using the Geant4 Monte Carlo simulation toolkit (Allison et al., 2006).The Taiji spacecraft model, a complex structure illustrated in Figure 4a, is based on the LISA spacecraft model (Papini et al., 1996).To construct our Taiji complex model for this study, we integrated Taiji's existing inertial sensor model with the peripheral electronics and casing from the LISA spacecraft.Over 200 volumes, representing components weighing more than 0.1 kg, were strategically placed throughout the spacecraft, utilizing materials currently available.The spacecraft's outer shell takes the form of a frustum, with the top diameter 2.7 m, the bottom diameter 2.17 m, and the height 0.5 m.The key optical components, including titanium chambers, molybdenum chambers, electrodes, TMs, and telescopes, are housed within the payload fairing.The core equipment, including the TMs, resides within the Y-shaped shield tubes, as depicted in Figure 4b.Taiji's inertial sensor comprises the TMs, electrodes, electrode chambers, and a vacuum chamber.In this model, the TM is a 46 × 46 × 46 mm alloy cube composed of 70% gold and 30% platinum, with a magnetic susceptibility of χ < 5 × 10 −5 .For our model in this paper, the vacuum density is set at 1.0 × 10 −25 g/cm 3 .During the simulation of cosmic ray particles, a spherical source with the radius 1,499 mm serves as an isotropic particle source, with particles incidenting on the entire spacecraft model following a cosine angular distribution.

Physical Processes
Given the high-energy nature of GCR and SPE, these particles can penetrate the spacecraft's outer materials and undergo intricate interactions, leading to the production of numerous secondary charged particles.To authentically simulate the charging process of the TMs in the GW detection spacecraft due to high-energy particle impacts, it is essential to track all secondary particles down to their lowest energy states.In this study, Monte Carlo simulations were conducted using Geant4.10.03.p03 to comprehensively track particles entering the spacecraft's TM and record information such as particle type, charge, and energy.As energy levels decrease, the associated physical processes also change.Multiple physical processes were considered in this research, including hadron processes (G4HadronPhysicsQGSP_BIC, G4HadronElasticPhysics, and G4IonPhysics), low-energy electromagnetic processes (G4EmStandardPhysics_option4), electro-nuclear and gamma-nuclear processes (G4EmExtraPhysics), and decay processes (G4DecayPhysics).The energy range spanned 11 orders of magnitude, from eV to hundreds of GeV.All particles generated in the simulations were tracked until they reached zero energy.For electromagnetic interaction processes, a threshold of 250 eV was typically set for secondary particle production to avoid excessive generation of secondary particles due to excessively low energies, preventing divergence issues.The secondary energy threshold for hadronic ionization usually corresponds to the average ionization energy of the material.To closely approximate the real reaction scenarios, this paper sets the secondary particle production threshold for all particles entering the inertial sensor to 250 eV, while the remaining thresholds were set at 1 mm due to limited computational resources.

Charging Simulation Results and Discussion
The net charging rate and effective charging rate of the TMs are critical output parameters derived from charging simulations, representing key factors contributing to TMs charging noise.We examined the net charging rate and effective charging rate of the Taiji complex model, considering the influence of GCR protons, 3 He, 4 He, and typical SPEs.The definitions of Taiji's TMs net charging rate and effective charging rate are as follows: where j is the number of charges deposited due to a single particle event and λ j is the probability of occurrence of these events.It can be seen that the positive and negative charges cancel out in the net charging rate calculation and only the net charge that is eventually deposited into the TMs is considered.Each positive and negative charge contributes to the effective charging rate by the definition of the effective charging rate.In particular, the spectral density of the charging bulk noise is expressed as a function of the effective charging rate.
where e is the elementary charge.

Test Masses Charging Results
In this investigation, we present a predictive analysis of TMs charging conditions in the context of the Taiji GWs detection mission, focusing on specific space environment conditions.Our approach combines the GCR model described in Section 2 with the SPE model and integrates these with the TMs charging simulation method detailed in Section 3.This multifaceted approach aims to ensure the precision and reliability of our predictions regarding the charging scenarios encountered by the Taiji spacecraft's TMs.
To achieve this, we have developed a sophisticated geometric model.Additionally, we have conducted Monte Carlo simulations to comprehensively trace the trajectories of all primary and secondary particles originating from cosmic ray sources, recording data on both incoming and outgoing positive and negative particles interacting with the TMs.Our study encompasses meticulous simulations of interactions between the spacecraft's materials and GCR of varying intensities, corresponding to different solar activity phases.Furthermore, we incorporated simulations for several typical SPEs.Specifically, we conducted simulations for both solar maximum and solar minimum conditions GCR protons and SPEs, with each simulation involving an impressive total of 1.0 × 10 9 events.Similarly, simulations for GCR 3 He and 4 He ions under solar maximum and solar minimum conditions included 5.0 × 10 8 events.The exposure time in our simulations ranged from a minimum of 3,200 s for GCR to a maximum of 260,000 s, while SPEs were simulated with exposure times ranging from seconds to tens of seconds.
Our analysis of TMs charging rates is based on rigorous statistical assessments of net charge deposition resulting from individual events.Figures 5 and 6 graphically represent histograms of net charge deposition for various ions from GCR under both solar maximum and solar minimum conditions.Notably, the majority of events led to a charge deposition of one unit of positive charge, followed by instances of one unit of negative charge and, occasionally, two units of positive charge.Over a series of events, the interaction of positive and negative charges consistently yielded a net positive charging rate.Figures 5 and 6 selectively highlight the events with net charging rates below ±10 +e and do not encompass all net charging events.Among the recorded events, the most extreme positive net charging event reached a charge deposition of +60 +e, while the most extreme negative net charging event exhibited a charge deposition of −59 +e.Importantly, observations reveal that under both solar maximum and solar minimum conditions, the net charging distributions resulting from individual events closely resembled each other.Additionally, the distribution of net charging from individual events during SPEs exhibited striking similarities to that of GCR protons.
In accordance with Equations 3 and 4, both the net charging rate and effective charging rate are derived from charge deposition events, while Equation 5 forms the basis for determining the spectral density of charging noise.Table 3 succinctly summarizes the charging rates and charging noise for solar maximum and solar minimum GCR.Evidently, under the most adverse conditions of solar minimum GCR, the total net charging rate is 34.5 ± 1.8 +e/s for TM1 and 33.9 ± 1.8 +e/s for TM2, respectively.Simultaneously, we anticipate total effective charging rates of 434.2 e/s for TM1 and 426.7 e/s for TM2.The computation of total charging noise levels results in values of 29.5 e/s/Hz 1/2 for TM1 and 29.2 e/s/Hz 1/2 for TM2.Moreover, under solar maximum conditions, we forecast that TM1 and TM2 will exhibit total net charging rates of 9.6 ± 0.5 +e/s and 9.6 ± 0.3 +e/s, respectively, alongside corresponding total effective charging rates of 274.1 e/s for TM1 and 279.5 e/s for TM2.In addition, we project total charging noise levels of 23.4 e/s/Hz 1/2 for TM1 and 23.6 e/s/Hz 1/2 for TM2.Notably, Table 3 provides a comprehensive overview of the charging rates for both TMs on a single GWs detection satellite, underscoring the remarkable consistency of our predictions.It is worth emphasizing that within the same environment, the charging rates for the two TMs exhibit nearly identical results, with a maximum net charging rate difference about 5.9%.
Charging predictions for typical SPEs are derived using a simulation process akin to that employed for GCR.The primary distinguishing factors revolve around differences in energy spectrum range and spectral flux.Table 4 displays the charging rates for five representative SPEs.Notably, there are substantial variations in charging rates attributed to these events.For instance, on 7 June 2011, a SPE generated net charging rates for TM1 and TM2, amounting to 798 ± 23 +e/s and 847 ± 20 +e/s, respectively.In contrast, the SPE of 29 September 1989, resulted in net charging rates of 76,674 ± 1,942 +e/s for TM1 and 76,320 ± 3,070 +e/s for TM2.This translates to a disparity in charging rates of nearly 100-fold, approximately 80 to 8,000 times higher than the net charging rate induced by solar maximum GCR.In the context of SPEs predictions, the maximum difference in net charging rates between the two TMs was 5.8% on 7 June 2011, while differences for other events remained within 1%.

Charging-Induced Acceleration Noise
During the process of charging cosmic ray particles, the spectral density of acceleration noise attributed to charge deposition can be delineated into two distinct components (Antonucci et al., 2012).The first component emerges when any residual charge is multiplied by random charge noise, resulting in electrostatic force noise at 0.1 mHz: Here,   1∕2  () stands for the density of random charge spectrum noise,   1∕2  corresponds to the density of charge Poisson noise spectrum, C T represents TM's total capacitance relative to its ambient surroundings,     denotes the capacitance gradient along the x-axis, and Δ x representing the potential deviation of TMs due to charging.
The second component pertains to the emergence of electrostatic force noise at a frequency of 0.1 mHz, resulting from fluctuations in the residual Δ x when multiplied by any non-zero TMs charge.Δ  pertains to the spectral noise density of the stray potential difference spectrum.Furthermore, the value of 10 7 +e can be seen as an estimation of the cumulative charge over a 2-day period, considering a reasonable discharge threshold.
The charging process of cosmic-ray particles is considered the most significant source of TM acceleration noise in space-based GW detectors.Taiji has set a total acceleration noise limit of 3 × 10 −15 m • s −2 • Hz −1/2 at 0.1 mHz, in alignment with the requirements of LISA (Vitale et al., 2002;Z. Luo et al., 2020).Acceleration noise induced by charging can be categorized into two distinct components, as expressed in Equations 6 and 7.For the first component,   1∕2  () is directly linked to the effective charging rate resulting from cosmicray particles, as expressed in Equation 6.Based on the effective charging rates reported in Tables 3 and 4 for GCR and SPEs, we project that under the most extreme conditions of GCR during solar minimum,   1∕2  () for TM1 will be 0.43 × 10 −15 m • s −2 • Hz −1/2 at 0.1 mHz, and for TM2, it will be 0.43 × 10 −15 m • s −2 • Hz −1/2 at 0.1 mHz.The acceleration noise resulting from the effective charging rate due to GCR is significantly below the total acceleration noise limit.Furthermore, we forecast the acceleration noise   1∕2  () for five typical SPEs.For the SPE on 7 June 2011, the acceleration noise   1∕2  () for TM1 and TM2 are 0.67 × 10 −15 m • s −2 • Hz −1/2 at 0.1 mHz and 0.66 × 10 −15 m • s −2 • Hz −1/2 at 0.1 mHz.As for the SPE on 29 September 1989, the corresponding acceleration noise   1∕2  () is 6.70 × 10 −15 m ⋅s −2 ⋅Hz −1/2 at 0.1 mHz for both TM1 and TM2.Equation 6provides the effective charging rate required to reach the acceleration noise limit, estimated at 20,833 e/s.Consequently, the acceleration noise arising from an effective charging rate exceeding 20,833 e/s for the SPE on 29 September 1989, significantly surpasses the limit.Moreover, addressing the acceleration noise induced by such high effective charging rates poses substantial challenges and would severely impact the scientific detection of GWs.For the second component, involves the spectral noise density of arbitrary non-zero TMs charge spectra, which is directly related to the cumulative charge of cosmic-ray particles within the TMs, as outlined in Equation 7. Leveraging the net charging rate data from Tables 3  and 4, we make predictions regarding the acceleration noise resulting from charge accumulation.For both solar maximum and solar minimum GCR, we estimate that the TMs will reach the discharge threshold of 10 7 +e within a timeframe ranging from 80.5 to 289.4 hr.In the case of SPEs with higher net charging rates, the threshold is reached in considerably shorter durations.For instance, the SPE on 29 September 1989, is expected to attain the threshold in approximately 130 s.Even in the case of the SPE on 7 June 2011, which exhibits the smallest net charging rate, the threshold will be reached in around 3.3 hr (Kenyon et al., 2021).
In scenarios of extreme solar activity, prompt proactive discharging measures are imperative to mitigate the impact on GWs scientific data.

Experimental Setup
The direct validation of TM charging using ground-based accelerators is a highly formidable task.Consequently, we turn to accelerator irradiation experiments to indirectly evaluate the error level of the simulation method.This approach enables us to verify the dependability and precision of the simulation in the real space environment.In these experiments, we employed the single-energy proton direct irradiation method to assess the TM, with charge measurements performed using a detection system.The experiments were carried out at the 50 MeV medium-energy proton cyclotron located at Huairou, China.As illustrated in Figure 7, the experimental apparatus are consisted of a proton beam system, vacuum system, and detection system.Within the vacuum system, a dedicated vacuum tank was utilized for the experiment.To guarantee the unhindered entry of the proton beam into the vacuum tank, we precision-machined a circular titanium window with a diameter of 10 cm and a thickness of 100 μm onto the vacuum tank, serving as the designated entry point for the proton beam.The proton accelerator generated a single-energy proton beam ranging from 30 to 50 MeV.The proton beam irradiation area covered 20 cm × 20 cm, with a flux varying from 5 × 10 5 to 5 × 10 9 p/cm 2 /s.After passing through a titanium window with a diameter of 10 cm and a thickness of 100 μm, the proton beam irradiated an aluminum TM measuring 46 × 46 × 46 mm, as depicted in Figure 8.In particular, we utilized polyimide high insulating material to isolate the TM and prevent the charge accumulated within it from draining.During the irradiation process, the beam area reduced, while the flux remained relatively stable.To enhance the precision of our validation, we utilized three proton beam initial energies: 30 MeV, 40 MeV, and 50 MeV.Throughout the experiment, the vacuum level inside the vacuum chamber was maintained below 1.2 × 10 −3 Pa and the duration of each proton irradiation was 2 min.We applied electromagnetic shielding to the signal transmission lines of the charge detection system.Following proton beam irradiation, a stepper motor controlled the movement platform's approach to the insulated TM, enabling physical contact between the charge detection probe and the TM.The accumulated charge on the TM was subsequently collected and analyzed using a KEITHLEY 6517B electrometer.We documented the charge accumulation on the TM under varying energy and beam intensity conditions.

Experimental Results
At the initiation of measurements, background charge readings for the electrometer in a vacuum environment were recorded.To ensure the experiment's reliability, background detection was carried out before each irradiation session.The background charge recorded by the electrometer consistently remained below 1 pC in the vacuum environment, with a minimum detectable charge of 1 fC.Seven independent trials were performed for each single-energy proton beam experiment, and the final results were calculated as the averages of these trials.The Monte Carlo simulations established the TM model with the same material and dimensions and proton beam conditions as the proton experiments, resulting in charge measurements for three single-energy proton beams.The results, as outlined in Table 5, exhibit good conformity between experimental and simulation findings, with relative errors below 10%.This underscores the close alignment of simulation outcomes with ground-based experimental results under equivalent shielding conditions and particle sources.

Conclusion
When operating in orbit, spacecraft dedicated to GWs detection encounted with the radiation environment of GCR and SPEs.These high-energy particles induce an electrical charge on the TMs of the core sensors, leading to acceleration noise that compromises the precision of scientific data collected for GWs detection.To accurately assess the impacts of GCR and SPEs on the charging of Taiji's TMs, we applied the Monte Carlo simulation of the charging process by GCR and SPEs using the Geant4 toolkit with constructing a sophisticated spacecraft model.By combining the CREME96 GCR spectrum with SPEs spectra obtained from GOES satellites, we investigated the charging conditions of the TMs under different solar activities.The computational results indicate that the prolonged  exposure to GCR generally results in manageable TMs charging, leading to relatively minor acceleration noise caused by charging that takes several days to several weeks to reach the charging threshold.However, isolated SPEs, with an effective charging rate exceeding 20,833 e/s, can trigger charging-induced acceleration noise surpassing Taiji's GWs detection accelerator noise limit, thus significantly compromising scientific detection.This threshold can be reached within a few minutes to a few hours for moderate intensity SPEs.
To verify the credibility of our simulations, we further applied the validation experiment by 30-50 MeV proton irradiation experiments.The experimental results are in good agreement with the corresponding simulation results.

Figure 2 .
Figure2.Differential energy spectra of Galactic cosmic rays proton, 3 He, and 4 He at 1 astronomical unit.

Figure 3 .
Figure 3. Proton fluxes of solar proton events and Galactic cosmic rays during solar maximum and solar minimum.

Figure 5 .
Figure 5. Individual event charging distributions from Galactic cosmic rays on (a) TM1 and (b) TM2 during solar minimum.

Figure 6 .
Figure 6.Individual event charging distributions from Galactic cosmic rays on (a) TM1 and (b) TM2 during solar maximum.

Figure 7 .
Figure 7. Schematic diagram of the experimental setup.

Figure 8 .
Figure 8.(a) The vacuum tank at the terminal of the proton beamline.(b) View of inside of the vacuum tank.

Table 3
) Summary of Test Masses Charging Due To Galactic Cosmic Rays 1∕2  (Δ)represents the spectral noise density corresponding to any non-zero TMs charge spectrum, and

Table 5
Experimental and Simulation Results of Proton Charging