Stopping Power Of Charged Particles Research Articles

Simulation study of cone-in-shell target for indirect-drive ion fast ignition concept under the theory of an effective interaction potential

The stopping power of charged particles released by the deuterium–tritium nuclear reactions has been extensively studied in the weakly to moderately coupled plasma regimes. We have modified the conventional effective potential theory (EPT) stopping framework to have a practical connection to investigate the ions energy loss characteristics in fusion plasma. Our modified EPT model differs from the original EPT framework by a coefficient of order 1 + {2 mathord{left/ {vphantom {2 {(5}}} right. kern-0pt} {(5}}ln overline{Xi }),(ln overline{Xi } is a velocity-dependent generalization of the Coulomb logarithm). Molecular dynamics simulations agree well with our modified stopping framework. To study the role of related stopping formalisms in ion fast ignition, we simulate the cone-in-shell configuration under laser-accelerated aluminum beam incidence. In ignition/burn phase, the performance of our modified model is in agreement with its original form and the conventional Li-Petrasso (LP) and Brown-Preston-Singleton (BPS) theories. The LP theory indicates the fastest rate in providing ignition/burn condition. Our modified EPT model with a discrepancy of sim 9%, has the most agreement with LP theory, while that of the original EPT (with a discrepancy of sim 47% to LP) and BPS (with a discrepancy of sim 48% to LP) methods maintain the third and fourth contributions in accelerating the ignition time, respectively.

Bohr's stopping-power formula derived for a classical free-electron gas

Bohr's centenary stopping-power formula is rederived for a free electron gas (FEG) system within the framework of nonrelativistic classical mechanics. A simple and more concise expression for the stopping power of charged particles in FEG is demonstrated on classical grounds. Using semiclassical arguments and the Euler-Maclaurin well-known mathematical formula, Bloch's correction that links Bethe's quantum theory to Bohr's classical model is also recovered. The proposed semiclassical stopping-power formula contains the main physical ingredients for a general stopping formula applicable for different systems and energies and facilitates computational calculations.

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons.

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

Stopping Power Modulation by Pump Waves of Charged Particles Moving above Two-Dimensional Electron Gases

The perturbation electron density and stopping power caused by the movement of charged particles above two-dimensional quantum electron gases (2DQEG) have been studied in numerous works using the quantum hydrodynamic (QHD) theory. In this paper, the QHD is modified by introducing the two-dimensional electron exchange-correlation potential at high density Vxc2DH and the pump wave modulations. Based on the modified QHD, the perturbation electron density and stopping power are calculated for pump waves with various parameters. The results show that the stopping power values are more accurate after considering Vxc2DH. Under the modulation of pump waves with the wavelength from 0.1nm to 0.1cm, the perturbation electron density of 2DQEG and the stopping power of charged particles show periodic changes. Under the modulation of pump waves with λ = 1.76 × 10−4 cm and Φ0=2×1010e/λf, the average stopping power with respect to the time phase θ becomes negative, which means that the charged particles will gain energy and can be accelerated. This is a new phenomenon in the fields of 2DQEG and of great significance in surface physics and surface modification in nanoelectronic devices with beam matter interactions.

Platform development for dE/dx measurements on short-pulse laser facilities

Generating benchmark data on charged-particle stopping power in dense plasma is a challenge, motivating new experimental platforms for facilities such as short-pulse lasers. We report on several experiments that aimed to develop a platform for high-precision stopping power measurements at OMEGA EP, specifically developing target-normal sheath acceleration (TNSA) sources, proton isochoric heating, and radiatively heated foams. Integrated experiments were performed to measure stopping power, but several phenomena have been identified that would need to be mitigated for a stopping-power measurement, including irreproducibility of the TNSA sources, spurious electromagnetic fields around proton-heated targets, and cross-talk between the source and subject targets. This work provides a basis for potential future work towards mitigating these problems and performing stopping-power measurements, and is also valuable data for general understanding of TNSA and proton isochoric heating experiments.

AbInitio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory.

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for abinitio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the abinitio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.

Tunable proton stopping power of deuterium-tritium by mixing heavy ion dopants for fast ignition

The theoretical model of charged-particle stopping power for the Coulomb logarithm lnΛb ≥ 2 plasma [Phys. Rev. Lett., 20, 3059 (1993)] is extended to investigate the transport of the energetic protons in a compressed deuterium-tritium (DT) pellet mixed with heavy ion dopants. It shows that an increase of mixed-ion charge state and density ratio results in the substantial enhancement of the proton stopping power, which leads to a shorter penetration distance and an earlier appearance of the Bragg peak with a higher magnitude. The effect of hot-spot mix on the proton-driven fast ignition model is discussed. It is found that ignition time required for a small mixed hot-spot can be significantly reduced with slightly increased beam energy. Nevertheless, the ignition cannot maintain for a long time due to increasing alpha-particle penetration distance and energy loss from mechanical work and thermal conduction at high temperatures.

ENERGY LEAKAGE PROBABILITY EFFECT ON IGNITION CONDITION IN AN INERTIAL CONFINEMENT FUSION PLASMA

For a weak to moderately coupled plasma, the charged particle stopping power dE/dx was recently calculated from first principles in Ref. 1 using the method of dimensional continuation.2 While the calculational techniques were imported from quantum field theory, the calculation itself lies squarely within the standard framework of convergent kinetic equations. By using these calculations, ignition condition regime in (D/Tx/3Hey) fusion fuel pellet is investigated, including energy deposition fraction of charged particles and neutrons in fuel pellet, bremsstrahlung and inverse bremsstrahlung radiation, inverse Compton scattering and thermal conduction losses.

NUCLEAR ELASTIC SCATTERING EFFECT ON STOPPING POWER OF CHARGED PARTICLES IN HIGH-TEMPERATURE MEDIA

By solving the Boltzmann equation, an expression is derived for the stopping power of fast ions via nuclear elastic scattering, taking into account the large-energy-transfer scattering effects. The plasma electrons and ions are considered in temperature equilibrium with the Maxwellian distribution function. Thus, by adding Coulomb stopping power, the complete treatment is obtained for stopping power of charged particles moving in a plasma. The result is used, for example, to calculate the stopping power of proton projectile moving in a deuterium–tritium plasma. These calculations show that the nuclear elastic scattering effect on stopping power of fast ions is more effective in high-temperature plasmas (T ≥ 10 keV) such as that used in thermonuclear plasmas.

Temperature equilibration in a fully ionized plasma: Electron-ion mass ratio effects

Brown, Preston, and Singleton (BPS) produced an analytic calculation for energy exchange processes for a weakly to moderately coupled plasma: the electron-ion temperature equilibration rate and the charged particle stopping power. These precise calculations are accurate to leading and next-to-leading order in the plasma coupling parameter and to all orders for two-body quantum scattering within the plasma. Classical molecular dynamics can provide another approach that can be rigorously implemented. It is therefore useful to compare the predictions from these two methods, particularly since the former is theoretically based and the latter numerically. An agreement would provide both confidence in our theoretical machinery and in the reliability of the computer simulations. The comparisons can be made cleanly in the purely classical regime, thereby avoiding the arbitrariness associated with constructing effective potentials to mock up quantum effects. We present here the classical limit of the general result for the temperature equilibration rate presented in BPS. In particular, we examine the validity of the m(electron)/m(ion)-->0 limit used in BPS to obtain a very simple analytic evaluation of the long-distance collective effects in the background plasma.

The energy partitioning of non-thermal particles in a plasma: the Coulomb logarithm revisited

The charged particle stopping power in a highly ionized and weakly to moderately coupled plasma has been calculated exactly to leading and next-to-leading accuracy in the plasma density by Brown, Preston and Singleton (BPS). Since the calculational techniques of BPS might be unfamiliar to some, and since the same methodology can also be used for other energy transport phenomena, we will review the main ideas behind the calculation. BPS used their stopping power calculation to derive a Fokker–Planck equation, also accurate to leading and next-to-leading orders, and we will also review this. We use this Fokker–Planck equation to compute the electron–ion energy partitioning of a charged particle traversing a plasma. The motivation for this application is ignition for inertial confinement fusion—more energy delivered to the ions means a better chance of ignition, and conversely. It is therefore important to calculate the fractional energy loss to electrons and ions as accurately as possible. One method by which one calculates the electron–ion energy splitting of a charged particle traversing a plasma involves integrating the stopping power dE/dx. However, as the charged particle slows down and becomes thermalized into the background plasma, this method of calculating the electron–ion energy splitting breaks down. As a result, it suffers a systematic error that may be as large as T/E0, where T is the plasma temperature and E0 is the initial energy of the charged particle. The formalism presented here is designed to account for the thermalization process and it provides results that are near-exact.

Kinetic study on self-energy and stopping power of charged particles moving in metallic carbon nanotubes

A semiclassical kinetic model is developed to simulate the plasmon excitation of nanotubes and the transport of charged particles moving through nanotubes. With the introduction of electron band structure, the analytical expressions of the dielectric function and the energy loss function are obtained for zigzag and armchair nanotubes of metallic properties, respectively. Numerical results display several very distinct peaks in the curves of loss function, showing effects from the collective excitation. Furthermore, the stopping power and self-energy are calculated while charged particles move along the axis of nanotubes with different geometries, under the influence of friction coefficients. For small enough friction coefficients, it can be regarded as a case with zero damping. But as the damping factor increases, not only the self-energy and stopping power decrease in magnitude, but also their extrema move to lower velocities, without distinct threshold effects.

Calculating the charged particle stopping power exactly to leading and next-to-leading order

I will discuss a new method for calculating transport quantities, such as the charged particle stopping power, in a weakly to moderately coupled plasma. This method, called dimensional continuation, lies within the framework of convergent kinetic equations, and it is powerful enough to allow for systematic perturbative expansions in the plasma coupling constant. In particular, it provides an exact evaluation of the stopping power to leading and next-to-leading order in the plasma coupling, with the systematic error being of cubic order. Consequently, the calculation is near-exact for a weakly coupled plasma, and quite accurate for a moderately coupled plasma. The leading order term in this expansion has been known since the classic work of Spitzer. In contrast, the next-to-leading order term has been calculated only recently by Brown, Preston, and Singleton (BPS), using the aforementioned method, to account for all short- and long-distance physics accurate to second order in the plasma coupling, including an exact treatment of the quantum-to-classical scattering transition. Under conditions relevant for inertial confinement fusion, BPS find the alpha particle range in the DT plasma to be about 30% longer than typical model predictions in the literature. Preliminary numerical studies suggest that this renders the ignition threshold proportionally higher, thereby having potential adverse implications for upcoming high energy density facilities. Since the key ideas behind the BPS calculation are possibly unfamiliar to plasma physicists, and the implications might be important, I will use this opportunity to explain the method in a pedagogical fashion.

Charged particle stopping power effects on ignition: Some results from an exact calculation

A completely rigorous first-principles calculation of the charged particle stopping power has recently been performed by Brown, Preston, and Singleton (BPS). This calculation is exact to leading and next-to-leading order in the plasma number density, including an exact treatment of two-body quantum scattering. The BPS calculation is therefore extremely accurate in the plasma regime realized during the ignition and burn of an inertial confinement fusion capsule. For deuterium-tritium fusion, the 3.5MeV alpha particle range tends to be 20%–30% longer than most models in the literature have predicted, and the energy deposition into the ions tends to be smaller. Preliminary numerical simulations indicate that this increases the ρR required to achieve ignition.

Effective quality factors for neutrons based on the revised ICRP/ICRU recommendations

The quality factor (Q) is intended to relate the biological effectiveness of a radiation to the absorbed dose delivered in tissue. Quality factors are defined as a function of the unrestricted linear energy transfer (L) relationship in water and are used with operational quantities. Radiation weighting factors (wR) are used in protection quantities to take into account total radiation detriment. While the International Commission on Radiological Protection (ICRP) defines the Q(L) relationship, the International Commission on Radiation Units and Measurements (ICRU) recommends the charged particle stopping power and range data. If either of these data recommendations change, the quality factors must be recomputed. The latest guidance from both organisations applicable to neutron quality factors are the ICRP Publication 60 (Q(L) relationship) and the ICRU Report 49 (stopping power and range data). In the present study, absorbed dose conversion coefficients (pGy cm2) were calculated for two operational quantities defined by the ICRU--the ambient absorbed dose and the personal absorbed dose. Dose-equivalent (pSv cm2) conversion coefficients were also computed using mean quality factors based on ICRP 60 and ICRU 49 recommendations. Effective quality factors were then calculated from the ratio of the dose-equivalent to the absorbed dose conversion coefficients for both the personal dose-equivalent and ambient dose-equivalent and compared to values reported in the literature.

Flight performance of EXAM — a balloon-borne detector to search for extragalactic antimatter

We describe the performance of the EXAM detector during its five hour balloon flight in 1988. EXAM is an experiment designed to search for cosmic rays of extragalactic origin which are made of antimatter. The EXAM technique to identify antinuclei is unique, being based on higher order corrections to electronic stopping power of charged particles, and on the response characteristics of CR-39 track-etch detectors, plastic scintillators, and Cherenkov radiators. Included in the present paper are the completed analysis of the electronic detectors, and preliminary results of the analysis of the track-etch detectors, including a demonstration of our ability to match particles identified with the drift tube tracking elements during the flight with their tracks found in the passive CR-39 detectors. When the CR-39 analysis is complete, we will have approximately 10 000 events for which antimatter analysis can be made.

Nonlinear hydrodynamic theory of electronic stopping power

We have formulated a fully nonlinear hydrodynamic theory of the electronic stopping power of charged particles in matter. In the zero velocity limit, our theory reduces to a Thomas-Fermi-Dirac-von Weiszäcker description of the electronic screening around an external point charge. With increasing velocity, the dynamic screening charge is obtained from a numerical solution of the hydrodynamic equations. We also introduce a fluid viscosity which allows one to simulate the single-particle excitations responsible for the low velocity stopping power. A comparison of our results for protons and antiprotons with linear response theory shows that nonlinearities in the screening are important for all velocities up to the stopping power maximum. In addition, comparison with earlier nonlinear quantum-mechanical calculations at low velocities shows that the hydrodynamic theory provides a realistic and accurate description of the stopping power phenomenon.

Fermi-degeneracy and discrete-ion effects in the spherical-cell model and electron-electron correlation effects in hot dense plasmas.

The spherical-cell model [F. Perrot, Phys. Rev. A 25, 489 (1982); M. W. C. Dharma-wardana and F. Perrot, ibid. 26, 2096 (1982)] is improved to investigate laser-produced hot, dense plasmas. The free-electron distribution function around a test free electron is calculated by using the Fermi integral in order that the free-electron--free-electron correlation function includes Fermi-degeneracy effects, and also that the calculation includes the discrete-ion effect. The free-electron--free-electron, free-electron--ion, and ion-ion correlation effects are coupled, within the framework of the hypernetted-chain approximation, through the Ornstein-Zernike relation. The effective ion-ion potential includes the effect of a spatial distribution of bound electrons. The interparticle correlation functions and the effective potential acting on either an electron or an ion in hot, dense plasmas are calculated numerically. The Fermi-degeneracy effect on the correlation functions between free electrons becomes clear for the degeneracy parameter \ensuremath{\theta}\ensuremath{\lesssim}1. The discrete-ion effect in the calculation of the correlation functions between free electrons affects the electron-ion pair distribution functions for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\gtrsim}3. As an application of the proposed model, the strong-coupling effect on the stopping power of charged particles [Xin-Zhong Yan, S. Tanaka, S. Mitake, and S. Ichimaru, Phys. Rev. A 32, 1785 (1985)] is estimated. While the free-electron--ion strong-coupling effect and the Fermi-degeneracy effect incorporated in the calculation of the free-electron distribution function around a test free electron enhance the stopping number, the quantum-diffraction effect incorporated in the quantal hypernetted-chain equations [J. Chihara, Prog. Theor. Phys. 72, 940 (1984); Phys. Rev. A 44, 1247 (1991); J. Phys. Condens. Matter 3, 8715 (1991)] reduces the stopping number substantially.

Stopping Power of Charged Particles I

AbstractThe stopping power of charged particles is determined in the random phase approximation using Lenard Balescu type collision integrals. The stopping power is closely related to other single particle properties such as self energy and quasi particle life time.In this part I, numerical evaluations are given for equal masses (of test and target particles).

Neutron radiography based on CN and CR nuclear track detectors

We describe the performance of the EXAM detector during its five hour balloon flight in 1988. EXAM is an experiment designed to search for cosmic rays of extragalactic origin which are made of antimatter. The EXAM technique to identify antinuclei is unique, being based on higher order corrections to electronic stopping power of charged particles, and on the response characteristics of CR-39 track-etch detectors, plastic scintillators, and Cherenkov radiators. Included in the present paper are the completed analysis of the electronic detectors, and preliminary results of the analysis of the track-etch detectors, including a demonstration of our ability to match particles identified with the drift tube tracking elements during the flight with their tracks found in the passive CR-39 detectors. When the CR-39 analysis is complete, we will have approximately 10 000 events for which antimatter analysis can be made.