Particle Tracing Code Research Articles

Simulation of charge-exchange induced NBI losses on EAST

The neutral beam injection is widely adopted in tokamaks as a key heating tool, playing a crucial role in generating burning plasmas. However, the loss of beam ions can damage the first wall and reduce the heating efficiency, resulting in failure to maintain steady-state conditions. In this work, the effect of neutral particles in the edge on fast ions generated by NBI in the Experimental Advanced Superconducting Tokamak (EAST) device is studied using the particle tracer code (PTC). The poloidal distribution of neutral particles is calculated by edge plasma simulation code SOLPS-ITER. In this simulation, four beam lines in EAST are considered: co-current tangential (co-tang), co-current perpendicular (co-perp), counter-current tangential (ctr-tang) and counter-current perpendicular (ctr-perp). It is shown that, in the absence of neutral particles, the loss fraction of ctr-injection is considerably higher than that of the co-injection. When considering the neutral particles, it is found that the ctr-perp injection demonstrates a significant variation in particles loss fraction (ranging from 18.56% to 25.42%) compared to the other three injection configurations. In terms of the loss fraction induced by neutral particles, ctr-injection exceeds co-injection, and perpendicular configuration exceeds tangential configuration. Furthermore, the difference of charge exchange ratios of three different energy (full energy, half energy, one third energy) of the four injections can be attributed to variations in the poloidal trajectories associated with each of these injections. Moreover, approximately half of fast ions which undergo neutralization directly lose to the first wall while the rest re-enter the bulk plasma and re-ionize. Except for the ctr-tang injection, the reionization ions from the other three injections exhibit effective confinement.

Transport characteristic evaluation of runaway electrons in an ITER disruption simulation

In previous studies, it has been observed that the transport of energetic electrons decreases with increasing energy. This observation is a global and long-time-scale result, attributed to the space-averaged perturbations. In this work, we focus on the local and instantaneous transport characteristics of runaway electrons (REs) during the phase of tokamak disruption, with REs speeds close to the speed of light. To simulate the dynamics of REs, we utilize a particle tracing code called PTC. By coupling PTC with the MHD code JOREK, we are able to study the energy and spatial dependence of RE transport. Our investigations reveal that the finite orbit width (FOW) effect plays an important role in RE transport. This effect is influenced by the relative direction of the electron drift and the magnetic field line. Specifically, the FOW effect strengthens the transport when the drift direction aligns with the deflecting direction of the field line. And we compare the transport profiles among three time slices: at the beginning of the thermal quench, during the thermal quench, and at the beginning of the current quench. In this ITER disruption simulation, the perturbation scale is strong and δB/B is up to 0.05 at developed thermal quench stage. It is reasonable that the influence of FOW effect on transport is less than that of magnetic perturbation even if the energy of REs is about hundreds MeV and the orbit width is equal to or greater than the perturbation length. These analyses provide insights into the mechanisms of RE transport based on magnetic perturbations.

Europa's Perturbed Fields and Induced Dipole Affect Energetic Proton Depletions During Distant Alfvén Wing Flybys

AbstractWe investigate the causes of energetic proton (80–540 keV) depletions measured during the two most distant flybys of Europa by Galileo, E17 and E25A, which encountered the Alfvén wings. First, by simulating the proton flux with a Monte Carlo particle tracing code we investigate the effect of: electromagnetic field perturbations, the induced dipole, atmospheric charge exchange and plumes. Inhomogeneous fields associated with the Alfvén wings and the ionosphere strongly affect the depletions. For homogeneous fields the depletion along the trajectory is focused on a narrow pitch angle range and has no structure, whereas the depletion for perturbed (inhomogeneous) fields represents a wider and complex structure. Furthermore, also the induced dipole alters the depletion structure. The effect of plumes (density 2.5 × 1015 m−3) and charge exchange on the proton depletion is minor. Second, we compare the simulations to the proton measurements. The simulations with inhomogeneous fields describe the data qualitatively better than the homogeneous case, suggesting that indeed field perturbations are responsible for the measured losses. We attribute discrepancies between the simulations and the proton measurements to discrepancies between the simulated and real fields. We argue that simulating the fields along the trajectory is a good first step, but that ideally the energetic ion flux is reconstructed well to gain confidence in the interpretation of the simulated magnetic field. In conclusion, energetic ion observations along distant flybys through the Alfvén wings are suitable for isolating the characteristics of the global configuration of the magnetospheric interaction region of Europa (or other moons).

Heat loads on the accelerator grids of the ITER HNB prototype

Among the heating and current drive system which are being developed for the ITER experimental reactor, 2 neutral beam injectors with a power of 16.5 MW each will be based on the acceleration of H−/D− ions up to the energy of 870 keV / 1 MeV. Dealing with an accelerated beam power up to 40 MW, beam divergence, aiming and homogeneity have to be optimized to avoid damaging the beamline components or the grids of the accelerator. The design of the ITER HNB prototype, MITICA, was based on the coupling of several codes starting from experimental inputs available at that time. Heat loads, in particular, were estimated by the 2D version of the code Monte Carlo particle tracing code EAMCC. In the last years, a 3D version of the same code was developed and the operation of negative ion sources for fusion increased the knowledge concerning those parameters which are fundamental to estimate the expected heat loads. In this work, calculations are performed by EAMCC3D and the role of different source and accelerator parameters, such as the negative ion temperature and the beam halo, is highlighted.

Numerical simulation of <inline-formula><tex-math id="Z-20231101091527">\begin{document}$\boldsymbol \alpha$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230700_Z-20231101091527.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230700_Z-20231101091527.png"/></alternatives></inline-formula> particle slowing-down process under CFETR scenario

The high-energy <i>α</i> particles produced by deuterium-tritium fusion are the primary heating source for maintaining high temperatures in future tokamak plasma. Effective confinement of <i>α</i> particles is crucial for sustaining steady-state burning plasma. The initial energy of <i>α</i> particles is <inline-formula><tex-math id="M1">\begin{document}$ 3.5 {\text{ MeV}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230700_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="21-20230700_M1.png"/></alternatives></inline-formula>. According to theoretical calculations, it takes approximately 1 second to slow down <i>α</i> particles through Coulomb collisions to an energy range similar to the energy range of the background plasma. In the slowing-down process, some <i>α</i> particles may be lost owing to various transport processes. One significant research problem is how to utilize <i>α</i> particles to effectively heat fuel ions so as to sustain fusion reactions in a reactor. Assuming local Coulomb collisions and neglecting orbital effects, a classical slowing-down distribution for <i>α</i> particles can be derived. However, considering the substantial drift orbit width of <i>α</i> particles and the importance of spatial transport, numerical calculations are required to obtain more accurate <i>α</i> particle distribution function. In this study, the particle tracer code (PTC) is used to numerically simulate the slowing-down process of <i>α</i> particles under different scenarios in the Chinese Fusion Engineering Test Reactor (CFETR). By combining particle orbit tracing method with Monte Carlo collision method, a more realistic <i>α</i> particle distribution function can be obtained and compared with the classical slowing-down distribution. The results show significant differences between this distribution function and the classical slowing-down distribution, particularly in the moderate energy range. Further analysis indicates that these disparities are primarily caused by the strong radial transport of <i>α</i> particles at these energy levels. The research findings hold profound implications for the precise evaluating of ability of <i>α</i> particles to heat the background plasma. Understanding and characterizing the behavior of <i>α</i> particles in the slowing-down process and their interaction with the plasma is critical for designing and optimizing future fusion reactors. By attaining a deeper comprehension of the spatial transport and distribution of <i>α</i> particles, it becomes possible to enhance the efficiency of fuel ion heating and sustain fusion reactions more effectively. This study establishes a foundation for subsequent investigations and evaluation of <i>α</i> particles as a highly efficient heating source for fusion plasmas.

Calculation of collisionless pitch-angle scattering of runaway electrons with synchrotron radiation via high-order guiding-centre equation

Recently, the collisionless pitch-angle scattering for relativistic runaway electrons (REs) in toroidal geometries such as tokamaks was discovered through a full orbit simulation approach (Liu et al., Nucl. Fusion, vol. 56, 2016, p. 064002), and it was then theoretically investigated that a new expression for the magnetic moment, including the second-order corrections, could essentially reproduce the so-called collisionless pitch-angle scattering process (Liu et al., Nucl. Fusion, vol. 58, 2018, p. 106018). In this paper, with synchrotron radiation, extensive numerical verification of the validity of the high-order guiding-centre theory is given for simulations involving REs by incorporating such an expression for the magnetic moment into our particle tracing code. A high-order guiding-centre simulation approach with synchrotron radiation (HGSA) is applied. Synchrotron radiation plays an essential role in the life cycle of REs. The energy of REs first increases and then becomes saturated until the electric field acceleration is balanced by the radiation dissipation. Unfortunately, the process cannot be simulated accurately with the standard guiding-centre model, i.e. the first-order guiding-centre model. Remarkably, it is found that the HGSA can effectively produce the fundamental process of REs. Since the time scale of the energy saturation of REs is close to seconds, the computational cost becomes significant. In order to save costs, it is necessary to estimate the time of energy saturation. An analytical estimate is derived for the time it takes for synchrotron drag to balance an accelerating electric field and the provided formula has been numerically verified. Test calculations reveal that HGSA is favourable for exploiting the dynamics of REs in tokamak plasmas.

Radial Transport of Energetic Electrons as Determined From the “Zebra Stripes” Measured in the Earth’s Inner Belt and Slot Region

The “zebra stripes” are drift-periodic structures present in the form of peaks and valleys in energetic (tens to hundreds of keV) electron spectrograms in the Earth’s inner belt and slot region. Their characteristics inform of preceding electric field disturbances. Specifically, their amplitude contains information on the radial transport of trapped particles generated by azimuthal electric field disturbances. We introduce a method to quantify radial transport from the measured amplitude of the zebra stripes, and we apply it to the zebra stripes observed on 16 February 2014. The findings are compared with results from a particle tracing code that leverages an empirical analytical model for the electric field disturbances. The measured amplitude of the zebra stripes indicates that the electric field disturbances transported the trapped population coherently, over radial distances spanning several hundreds to thousands of kilometers. The magnitude of radial transport is shown to depend on angular drift frequency and initial location (equatorial radial distance and magnetic local time) in the disturbance. The model-observation comparison suggests that the timing for electric field variations provided by the model is valid for studying radial transport in the inner belt and slot region. On the other hand, we found discrepancies when comparing radial transport magnitudes. When assuming that radial transport varies as L3, as weakly suggested by the data for set angular drift frequencies, and extrapolating observations to L = 1, the amount of experimental transport obtained is two to three times greater than numerical estimates. Outputs from the standalone version of the Rice Convection Model (RCM) suggests that the electric field disturbances are likely greater than the estimates provided by the empirical model. RCM also supports the idea that radial transport driven by the prompt penetration of magnetospheric convection varies as L3 in the inner belt and slot region.

Modeling Interactions of Narrowband Large Amplitude Whistler-mode Waves with Electrons in the Solar Wind inside ∼0.3 au and at 1 au Using a Particle Tracing Code

Abstract The discovery of large amplitude narrowband whistler-mode waves at frequencies of tenths of the electron cyclotron frequency in large numbers both inside ∼0.3 au and at ∼1 au provides an answer to longstanding questions about scattering and energization of solar wind electrons. The waves can have rapid nonlinear interactions with electrons over a broad energy range. Counter propagation between electrons and waves is not required for resonance with the obliquely propagating waves in contrast to the case for parallel propagation. Using a full 3D particle tracing code, we have examined interactions of electrons with energies from 0 eV to 2 keV with whistler-mode waves with amplitudes of 20 mV m−1 and propagation angles from 0° to 180° to the background magnetic field. Interactions with wave packets and single waves are both modeled based on observations at ∼0.3 au and 1 au. A test particle simulation approach allows us to examine the particle motion in detail, which reveals kinetic effects of resonant interactions. The simulations demonstrate the key role played by these waves in rapid scattering and energization of electrons. Strong scattering and energization for some initial energy and pitch angle ranges occurs for both counter-propagating and obliquely propagating waves. Strong scattering of strahl electrons counteracts the pitch angle narrowing due to conservation of the first adiabatic invariant as electrons propagate from the Sun into regions of smaller magnetic field. Scattering also produces the hotter isotropic halo. The concomitant limiting of the electron heat flux is also relevant in other astrophysical settings.

Numerical simulation and experiment of error field measurement using luminous trace of electron beam in SST-1

In contrast to the earlier experiments conducted in other machines, here, in SST-1 the error field measurement experiment is performed with a filled gas pressure ∼8 × 10−4 mbar which helped to create a luminescent toroidal beam of electron path originated due to impact excitation and guided by the toroidal magnetic field. Beam path deviations are observed and recorded from radial and top ports using visible range cameras. Such creation and detection of the electron beam path differs from the earlier works where the gun emitted electron beam deviation in ultra-high vacuum was detected on a collector-grid/fluorescent screen. In the present experiment, large beam deviations were observed. Later investigation of the experimental set-up reveals existence of a possible source of radial electric field in between the source and the vacuum vessel which are separately grounded. Thus, to understand the observed phenomena, experiments are numerically modeled with deviated TF coil set, PF coil set and the electron source location. A particle tracing code is used to follow the electron path in the magnetic field generated by the coil set of interest. Simulation results suggest that the large deviation corresponds to the E × B drifts and not due to the large field errors. Toroidally averaged field errors of the SST-1 TF coils at toroidal field of B0 = 15 kG are negligibly small ∼B0 × 10−6 or less, which should not adversely affect the plasma performance.

Analytical Chorus Wave Model Derived from Van Allen Probe Observations

AbstractChorus waves play an important role in the dynamic evolution of energetic electrons in the Earth's radiation belts and ring current. Using more than 5 years of Van Allen Probe data, we developed a new analytical model for upper‐band chorus (UBC; 0.5fce < f < fce) and lower‐band chorus (LBC; 0.05fce < f < 0.5fce) waves, where fce is the equatorial electron gyrofrequency. By applying polynomial fits to chorus wave root mean square amplitudes, we developed regression models for LBC and UBC as a function of geomagnetic activity (Kp), L, magnetic latitude (λ), and magnetic local time (MLT). Dependence on Kp is separated from the dependence on λ, L, and MLT as Kp‐scaling law to simplify the calculation of diffusion coefficients and inclusion into particle tracing codes. Frequency models for UBC and LBC are also developed, which depends on MLT and magnetic latitude. This empirical model is valid in all MLTs, magnetic latitude up to 20°, Kp ≤ 6, L‐shell range from 3.5 to 6 for LBC and from 4 to 6 for UBC. The dependence of root mean square amplitudes on L are different for different bands, which implies different energy sources for different wave bands. This analytical chorus wave model is convenient for inclusion in quasi‐linear diffusion calculations of electron scattering rates and particle simulations in the inner magnetosphere, especially for the newly developed four‐dimensional codes, which require significantly improved wave parameterizations.

Experimental analysis of the relationship between reverberant acoustic intensity and energy density inside long rooms.

In this paper, the validity of the Fick's law of diffusion in room acoustics is experimentally investigated inside long rooms. The room-acoustics diffusion model relies on Fick's law stating a proportionality relationship between sound intensity and energy density gradient inside a room through a constant diffusion coefficient. This relationship is investigated in the stationary state for the particular case of long rooms with different amounts of boundary scattering. Measurements were performed inside a 1:16 scale model, using a p-u sound intensity probe (calibrated with digital filters) to collect concurrent data in terms of sound pressure and axial velocity components. Then for each receiver position, sound intensity and energy density gradient were derived. The results show that inside long rooms the diffusion coefficient is not a constant but increases with the distance from the source with a slope depending on the scattering coefficient of the walls. Numerical simulations of the enclosures were performed too by using a sound particle-tracing code; a substantial agreement with the experimental findings is observed. The results imply that for such long enclosures, the diffusion model should consider a space-varying diffusion coefficient to be more consistent with real phenomena.

Accounting for the effect of diffuse reflections and fittings within street canyons, on the sound propagation predicted by ray tracing codes

Diffusion on building facades and fittings within a street can significantly affect sound propagation in urban areas. These phenomena are however not reproduced by the widespread outdoor sound propagation models that are based on ray codes algorithms, because their modeling would induce increased computational costs. In this paper, a set of 32 175 simulations is achieved with a sound particle tracing code to quantify the errors made when neglecting acoustic diffusion within street canyons, according to the street geometry (width, height, distance between the point source and the receiver), the acoustical properties of the street (diffusion and absorption coefficient of the facades, absorption coefficient of the ground), and the acoustical properties of the fittings (mean free path and average absorption coefficient), in the case of a receiver height of 1.5m. The diffuse reflections can lead to reduction of 2dB to an increase of 4dB of sound pressure levels in the absence of fittings, and can lead to an increase of 10dB of sound pressure levels in the presence of fittings, for the most unfavorable configurations. The influence of the acoustical parameters and the influence of the street geometry on sound attenuation are closely linked to each other. Moreover, acoustic diffusion results in an overall sound level increase if one considers a linear point source distribution. Finally, regressions are proposed that estimate the impact of diffusive reflections and street fittings on sound propagation as a function of the input parameters. These regressions can now be advantageously used to refine sound levels estimations within street canyons, when using classical outdoor sound propagation models, in the range of the parameters tested.

Compact femtosecond electron diffractometer with 100 keV electron bunches approaching the single-electron pulse duration limit

We present the design and implementation of a highly compact femtosecond electron diffractometer working at electron energies up to 100 keV. We use a multi-body particle tracing code to simulate electron bunch propagation through the setup and to calculate pulse durations at the sample position. Our simulations show that electron bunches containing few thousands of electrons per bunch are only weakly broadened by space-charge effects and their pulse duration is thus close to the one of a single-electron wavepacket. With our compact setup, we can create electron bunches containing up to 5000 electrons with a pulse duration below 100 fs on the sample. We use the diffractometer to track the energy transfer from photoexcited electrons to the lattice in a thin film of titanium. This process takes place on the timescale of few-hundred femtoseconds and a fully equilibrated state is reached within 1 ps.

On the meniscus formation and the negative hydrogen ion extraction from ITER neutral beam injection relevant ion source

The development of a large area (Asource,ITER = 0.9 × 2 m2) hydrogen negative ion (NI) source constitutes a crucial step in construction of the neutral beam injectors of the international fusion reactor ITER. To understand the plasma behaviour in the boundary layer close to the extraction system the 3D PIC MCC code ONIX is exploited. Direct cross checked analysis of the simulation and experimental results from the ITER-relevant BATMAN source testbed with a smaller area (Asource,BATMAN ≈ 0.32 × 0.59 m2) has been conducted for a low perveance beam, but for a full set of plasma parameters available. ONIX has been partially benchmarked by comparison to the results obtained using the commercial particle tracing code for positive ion extraction KOBRA3D. Very good agreement has been found in terms of meniscus position and its shape for simulations of different plasma densities. The influence of the initial plasma composition on the final meniscus structure was then investigated for NIs. As expected from the Child–Langmuir law, the results show that not only does the extraction potential play a crucial role on the meniscus formation, but also the initial plasma density and its electronegativity. For the given parameters, the calculated meniscus locates a few mm downstream of the plasma grid aperture provoking a direct NI extraction. Most of the surface produced NIs do not reach the plasma bulk, but move directly towards the extraction grid guided by the extraction field. Even for artificially increased electronegativity of the bulk plasma the extracted NI current from this region is low. This observation indicates a high relevance of the direct NI extraction. These calculations show that the extracted NI current from the bulk region is low even if a complete ion–ion plasma is assumed, meaning that direct extraction from surface produced ions should be present in order to obtain sufficiently high extracted NI current density. The calculated extracted currents, both ions and electrons, agree rather well with the experiment.

Activity‐dependent global model of electron loss inside the plasmasphere

Using data from the CRRES plasma wave experiment, we develop quadratic fits to the mean of the wave amplitude squared for plasmaspheric hiss as a function of Kp, L, and magnetic latitude (λ) for the dayside (6 < magnetic local time (MLT) ≤ 21) and nightside (21 < MLT ≤ 6) magnetic local time sectors. The empirical model of hiss waves is used to compute quasi-linear pitch angle diffusion coefficients for energetic, relativistic, and ultrarelativistic electrons in the energy range of 1 keV to 10 MeV. In our calculations, we account for changes in hiss wave normal angle and plasma density with increasing λ. Electron lifetimes are then calculated from the diffusion coefficients and parameterized as a function of energy, Kp, and L. Coefficients for both the hiss model and the electron lifetimes are provided and can be easily incorporated into existing diffusion, convection, and particle tracing codes.

Model of lifetimes of the outer radiation belt electrons in a realistic magnetic field using realistic chorus wave parameters

AbstractThe outer radiation belt electrons in the inner magnetosphere show high variability during the geomagnetically disturbed conditions. Quasi‐linear diffusion theory provides both a framework for global prediction of particle loss at different energies and an understanding of the dynamics of different particle populations. It has been recently shown that the pitch angle scattering of electrons due to wave‐particle interaction with chorus waves modeled in a realistic magnetic field may be significantly different from those estimated in a dipole model. In this work, we present the lifetimes of 1 keV–2 MeV electrons computed in the Tsyganenko 89 magnetic field model for the night, dawn, prenoon, and postnoon magnetic local time (MLT) sectors for different levels of geomagnetic activity and distances. The lifetimes in the realistic field are also compared to those computed in the dipole model. We develop a realistic chorus lower band and upper band wave models for each MLT sector using the recent statistical studies of wave amplitude, wave normal angle, and wave spectral density distributions as functions of magnetic latitude, distance, and Kp index. The increase of plasma trough density with increasing latitude is also included. The obtained in the Tsyganenko 89 field electron lifetimes are parameterized and can be used in 2‐D/3‐D/4‐D convection and particle tracing codes.

Extremely intense ELF magnetosonic waves: A survey of polar observations

AbstractA Polar magnetosonic wave (MSW) study was conducted using 1 year of 1996–1997 data (during solar minimum). Waves at and inside the plasmasphere were detected at all local times with a slight preference for occurrence in the midnight‐postmidnight sector. Wave occurrence (and intensities) peaked within~±5° of the magnetic equator, with half maxima at ~±10°. However, MSWs were also detected as far from the equator as +20° and 60° MLAT but with lower intensities. An extreme MSW intensity event of amplitude Bw = ~± 1 nT and Ew = ~± 25 mV/m was detected. This event occurred near local midnight, at the plasmapause, at the magnetic equator, during an intense substorm event, e.g., a perfect occurrence. These results support the idea of generation by protons injected from the plasma sheet into the midnight sector magnetosphere by substorm electric fields. MSWs were also detected near noon (1259 MLT) during relative geomagnetic quiet (low AE). A possible generation mechanism is a recovering/expanding plasmasphere engulfing preexisting energetic ions, in turn leading to ion instability. The wave magnetic field components are aligned along the ambient magnetic field direction, with the wave electric components orthogonal, indicating linear wave polarization. The MSW amplitudes decreased at locations further from the magnetic equator, while transverse whistler mode wave amplitudes (hiss) increased. We argue that intense MSWs are always present somewhere in the magnetosphere during strong substorm/convection events. We thus suggest that modelers use dynamic particle tracing codes and the maximum (rather than average) wave amplitudes to simulate wave‐particle interactions.

Kinetic effects of inclined magnetic field on physical sputtering by impurity ions

Sputtering caused by particle flux onto plasma-facing components is an essential physics for impurity transport codes. Velocity distribution of incident particles was obtained to calculate the yield from fluid quantities, i.e. plasma density and temperature. Effects of inclined magnetic field on incident angle distribution of impurity ions and sputtering yield were investigated with the aid of a particle tracing code with background electric field calculated by a PIC (Particle-In-Cell) simulation code. Simulations with various magnetic field angle and combination of projectile and target atoms were carried out. The most prominent parameter enhancing the yield is magnetic field angle. Large angle from the surface normal causes 3–5 times larger yield especially in the case of self sputtering. In the case of small mass ratio such as carbon on tungsten , the enhancement effect of the magnetic field is weak.

Stability analysis of a two-stage tapered gyrotron traveling-wave tube amplifier with distributed losses

The two-stage tapered gyrotron traveling-wave tube (gyro-TWT) amplifier has achieved wide bandwidth in the millimeter wave range. However, possible oscillations in each stage limit this amplifier's operating beam current and thus its output power. To further enhance the amplifier's stability, distributed losses are applied to the interaction circuit of the two-stage tapered gyro-TWT. A self-consistent particle-tracing code is used for analyzing the beam-wave interactions. The stability analysis includes the effects of the wall losses and the length of each stage on the possible oscillations. Simulation results reveal that the distributed-loss method effectively stabilizes all the oscillations in the two stages. Under stable operating conditions, the device is predicted to produce a peak power of 60 kW with an efficiency of 29% and a saturated gain of 52 dB in the Ka-band. The 3-dB bandwidth is 5.7 GHz, which is approximately 16% of the center frequency.

On Modeling Weak Sinks in MODPATH

Regional groundwater flow systems often contain both strong sinks and weak sinks. A strong sink extracts water from the entire aquifer depth, while a weak sink lets some water pass underneath or over the actual sink. The numerical groundwater flow model MODFLOW may allow a sink cell to act as a strong or weak sink, hence extracting all water that enters the cell or allowing some of that water to pass. A physical strong sink can be modeled by either a strong sink cell or a weak sink cell, with the latter generally occurring in low-resolution models. Likewise, a physical weak sink may also be represented by either type of sink cell. The representation of weak sinks in the particle tracing code MODPATH is more equivocal than in MODFLOW. With the appropriate parameterization of MODPATH, particle traces and their associated travel times to weak sink streams can be modeled with adequate accuracy, even in single layer models. Weak sink well cells, on the other hand, require special measures as proposed in the literature to generate correct particle traces and individual travel times and hence capture zones. We found that the transit time distributions for well water generally do not require special measures provided aquifer properties are locally homogeneous and the well draws water from the entire aquifer depth, an important observation for determining the response of a well to non-point contaminant inputs.