船木 一幸

A Rotating Detonation Engine (RDE) has higher thermal efficiency and simpler structure than a conventional gas turbine engine. Therefore, many research institutions has been investigating RDEs. Property of propagation of detonation waves in a RDE, however, has not been fully elucidated yet. Toward the practical use of RDEs, clarifying the propagation characteristics of detonation waves in RDEs is important. In the present study,we fabricated a plane RDE combustor with a cylindrical wall injector and performed visualization experiment. Propagation speed of the combustion waves that was observed in this experiment had reached to about 1300 - 1100 m/s, that is about 55 - 45 % of Chapman - Jouguet detonation velocity.

The authors measured thrust forces of an inductively coupled plasma thruster under various conditions of electric power and mass flow rate. The forward power from an RF power source is set in the range from 200 to 600 W and the mass flow rate is ranged from 0.09 to 0.17 g/sec. Ar gas is used as a propellant. The emission spectrum of the plasma is also obtained under various conditions. The thrust force did not increase for low forward powers and high mass flow rates because of insufficient Joule heating in the thruster. The thrust force and the specific impulse for high input powers or low mass flow rates are larger than those without the electric power because of the increment of stagnation temperature of the propellant. The thrust force also increases with the mass flow rate, while the specific impulse hardly changes for the variation of mass flow rate. This result denotes the stagnation temperature of the propellant scarcely varies with mass flow rate in this experiment. Results of the emission spectroscopy indicate that the plasma in the thruster is in a state of thermal non-equilibrium. The electron energy is, therefore, not probably transferred to heavy particles sufficiently.

We designed a rotary valve for a multi-cylinder pulse detonation rocket engine (PDRE), and constructed a greatly simplified rotary-valved four-cylinder PDRE (inner diameter and length of detonation tube: 37mm and 1,600 mm, respectively). The partial-fill effect of a propellant in a multi-cylinder PDRE under high-frequency operation was investigated. The suctioned-air fill fraction was estimated using the model of Sato et al., which is a semiempirical formula for the partial-fill effect of a propellant based on two-dimensional numerical analysis [Sato et al., Journal of Propulsion and Power, Vol. 22, No. 1, 2006, pp. 64-69]. A maximum propellant-based specific impulse of 251 s and a time-averaged thrust of 242N were achieved using C2H4-O-2 as the propellant and an operation frequency of 129.6 Hz/tube (fill pressure: 1 atm). The maximum operation frequency was 160.3 Hz/tube (641.2 Hz/all tubes).

© 2014 AIP Publishing LLC. We examined the plasma flow response to meso- and microscale magnetic dipoles by performing three-dimensional full particle-in-cell simulations. We particularly focused on the formation of a magnetosphere and its dependence on the intensity of the magnetic moment. The size of a magnetic dipole immersed in a plasma flow can be characterized by a distance L from the dipole center to the position where the pressure of the local magnetic field becomes equal to the dynamic pressure of the plasma flow under the magnetohydrodynamics (MHD) approximation. In this study, we are interested in a magnetic dipole whose L is smaller than the Larmor radius of ions riL calculated with the unperturbed dipole field at the distance L from the center. In the simulation results, we confirmed the clear formation of a magnetosphere consisting of a magnetopause and a tail region in the density profile, although the spatial scale is much smaller than the MHD scale. One of the important findings in this study is that the spatial profiles of the plasma density as well as the current flows are remarkably affected by the finite Larmor radius effect of the plasma flow, which is different from the Earth'S magnetosphere. The magnetopause found in the upstream region is located at a position much closer to the dipole center than L. In the equatorial plane, we also found an asymmetric density profile with respect to the plasma flow direction, which is caused by plasma gyration in the dipole field region. The ion current layers are created in the inner region of the dipole field, and the electron current also flows in the region beyond the ion current layer because ions with a large inertia can closely approach the dipole center. Unlike the ring current structure of the Earth's magnetosphere, the current layers in the microscale dipole fields are not circularly closed around the dipole center. Since the major current is caused by the particle gyrations, the current is independently determined to be in the direction of the electron and ion gyrations, which are the same in both the upstream and downstream regions. The present analysis on the formation of a magnetosphere in the regime of a microscale magnetic dipole is significant for understanding the solar wind response to the crustal magnetic anomalies on the Moon surface, such as were recently observed by spacecraft.

© 2014 IOP Publishing Ltd. We modelled the screening currents (Is) induced in high-temperature superconducting (HTS) coils to develop a method for the characterization and design of HTS magnets for space applications. The analysis made use of so-called percolation depinning and flux creep models to describe the current density versus the electric field in HTS tapes. We compared the model results with the experimental data obtained from a Bi-2223/Ag double pancake coil. The experimental residual magnetization due to the Isin the Bi-2223/Ag coil can be effectively modelled, assuming an equivalent loop length of approximately 9 mm for the Isin the coil. The values calculated from the method quantitatively agreed with the results for various experimental conditions. We also successfully modelled the hysteresis of the magnetization due to the Is. These results demonstrate the validity of our model for the Is, which considers the effects of flux creep and smaller Isloops in the multi-filamentary Bi-2223/Ag tape.

This study investigated the transport ac loss in a high-temperature superconducting (HTS) coil under ac ripple currents with de offsets for space applications of the Furs coil. We developed an analysis method to evaluate the effective ac loss in the HTS coil on the basis of the percolation depinning model. Our analysis clarified that larger de offsets greatly increase the effective ac loss even under a smaller ac current. In addition, we investigated the effect of the ac loss with the ripple current on the thermal behavior of a conduction-cooled Bi-2223/Ag coil. As a result, the ac loss decreased the thermal stability of the conduction-cooled coil in case that HTS tapes in the coil are in the flux-flow state such as the load factor of 80%. However, at a lower load factor such as less than 60%, the ripple current did not have much effect on the thermal stability of the conduction-cooled coil because most of the ac power were consumed as a reactive power. These results suggested that, in order to apply the ac ripple current to HTS coils, the operational load factor must be properly selected. This study leads to a design of the light-weight HTS coil system for space missions.

Helicon plasma sources are very useful in many aspects and are applicable to many fields across science and technology, as they can supply high-density (similar to 10(13) cm(-3)) plasmas with a broad range of external operating parameters. In this paper, developed, featured sources with various sizes are characterized along with discussions on their particle production efficiency. This paper aims to develop systems that can realize schemes with completely electrodeless plasma production and acceleration. This is expected to mitigate the existing problems of the finite lifetimes inherent in electric plasma propulsion tools. Experimental and theoretical approaches that implement such schemes are presented.

Magneto Plasma Sail (MPS) is one of the next generation space propulsion systems which generates a propulsive force using the interaction between the solar wind plasma and an artificial inflated magnetosphere generated by a superconductive coil. In the MPS system, the magnetosphere as a sail must be inflated by the plasma injection from the spacecraft in order to obtain the thrust gain. In the present study, the magnetic inflation concept is numerically tested by so-called ion one-component plasma model. As a simulation result, the magnetic moment of the system is drastically increased up to 45 times that of the coil current at plasma-β = 20 and rLi/L (radius of gyro motion / characteristics length of the magnetic field) = 0.01, and this is the first successful magnetosphere inflation obtained by numerical simulation. Corresponding maximum thrust gain is also estimated to be about 45. © 2014 The Japan Society of Plasma Science and Nuclear Fusion Research.

A magnetic sail is spacecraft propulsion that produces an artificial magnetosphere to block solar wind particles and thus impart momentum to accelerate a spacecraft. In the present study, the authors conducted two-dimensional particle-in-cell simulations on small-scale magnetospheres to investigate thrust characteristics of a magnetic sail and its derivative, magnetoplasma sail, in which the magnetosphere is inflated by an additional plasma injection. As a result, the authors found that the electron Larmor motion and the charge separation become significant on such a small-scale magnetosphere and the thrust of the magnetic sail is affected by the cross-sectional size of the charge-separated magnetosphere. The authors also reveal that the plasma injection, on the condition that the kinetic energy of plasma is smaller than the local magnetic field energy (approximate to 10-3), can significantly inflate the magnetosphere by inducing diamagnetic current in the same direction as the onboard coil current. As a result, the magnetoplasma sail thrust is increased effectively by an additional plasma injection: the magnetoplasma sail thrust (15N/m) becomes up to 7.5 times larger than the original thrust of the magnetic sail (2.0N/m). In addition, they found that the thrust gain of the magnetoplasma sail, defined as magnetoplasma sail thrust/(magnetic sail thrust+plasma injection thrust) becomes up to 2.2.

A magnetic sail is a spacecraft propulsion system that generates an artificial magnetosphere to block solar wind particles and uses the imparted momentum to accelerate a spacecraft. In the present study, three-dimensional particle-in-cell simulations were conducted on small-scale magnetospheres to investigate the thrust characteristics of small-scale magnetic sails. The results show that electron Larmor motion and charge separation become significant in small-scale magnetospheres, and that the thrust of the magnetic sail is affected by the cross-sectional area of the charge-separated plasma cavity. Empirical formulas for the thrust are obtained by changing spacecraft design and solar wind parameters. These equations show that the thrust of a small-scale magnetic sail is approximately proportional to magnetic moment, solar wind density, and solar wind velocity. The empirical formulas enable determination of the trajectory of the spacecraft and performance of a mission analysis.

In order to realize long-lived electric propulsion systems, we have been investigating an electrodeless plasma thruster. In our concept, high-density helicon plasma is accelerated by a magnetic nozzle for thrust production. In order to improve the thrust performance with simple systems, high magnetic flux density magnetic nozzle formed by permanent magnets is employed to our laboratory model plasma thruster. A magnetic circuit, which has high magnetic flux density up to 0.2 T at the magnetic nozzle throat, is constructed by permanent magnets and magnetic yoke. In order to investigate the thrust performance of this thruster, the thrust force is measured by a torsion-pendulum type thrust stand. From the thrust measurement, the thrust force and specific impulse increases with the RF power input. The thrust efficiency is drastically improved by increasing the RF power input, and it is considered to be caused by the discharge mode transition from the CCP to the ICP. The maximum thrust force and thrust efficiency of 2.7 ± 0.4 mN and 0.26 % is measured when the Ar gas mas flow rate is 1.2 mg/s, and plasma production frequency and power is 13.56 MHz and 1000 W.

Plasma flows in a 100-kWe-class, steady-state, self-field magnetoplasmadynamic (MPD) thruster were simulated by a plasma flow solver coupled with an electrode sheath model, which enables us to evaluate electrode fall voltages quantitatively. In this paper, influences of the coupling with the electrode sheath model on discharge pattern are discussed as well as dependences of thruster performances on the propellant mass flow rate and the discharge current. By the coupling, it is shown that a thrust is not significantly affected while a discharge voltage is increased attributed to a cathode fall voltage comparable with a potential fall just in the bulk plasma. The thrust and discharge voltage evaluated with the electrode sheath roughly agree with existing experimental results. For an argon mass flow rate of 2.0 g/s and a discharge current of 8 kA, the average cathode fall voltage was estimated to be 7.1 V, which is comparable with the average bulk fall voltage (7.1 V). Thus, it can be said that energy consumption within the cathode sheath is a significant loss factor of the MPD thruster.

Preliminary analysis of a mega-watt-class self-field MPD thruster head is conducted to conceptually design an MPD thruster system. It was found that thruster design was severely limited by the temperatures of electrode materials, and hence, thrust efficiency of the thruster head is restricted by heat ejection capability. To improve heat rejection capability, heat pipes are employed to thermally connect the electrodes and radiation panels. Through parametric survey of various thruster configurations, thrust efficiency as much as 38% was obtained for an Isp of 3,900s for hydrogen propellant.

A 1 kW class magnetic layer type Hall thruster designed for high specific impulse operation by IHI Corporation, Japan was modeled by a fully kinetic particle code. The measured maximum performance of the thruster was 64% in anode efficiency and 3,200s (3.1kW, 800V) in anode specific impulse. The thruster performance, wall heat loss and erosion, and the plasma property distributions were numerically investigated for the operation conditions ranged from 300V to 700V in discharge voltage, and 2mg/s to 4mg/s in xenon mass flow rate. Simulations with two numerical models: with and without the Bohm diffusion assumption were performed for each thruster operation conditions to characterize the uncertainty caused by the Bohm diffusion model. The simulation results were compared with the measured results, and exhibited excellent agreement with the maximum performance error of 20% for both models. It is suggested that as engineering tools, with and without Bohm simulations can be respectively used as the worst and best case analysis for the performance, heat load, and erosion.

A pulse detonation engine (Pulse Detonation Engine, PDE) generates a detonation wave intermittently, and obtains a thrust and work. In this research, the four cylinder pulse detonation rocket engine system “Todoroki II” was developed. The total weight of the flight test demonstrator is 32.5 kg. Moreover, the length is 1910 mm and the diameter of a combustion tube of a pipe in 800 mm is 37 mm. The launch and the recovery system for a flight test were also developed. The flight vehicle is recoveried without damage by winding system. It was proved that the flight test can be done repeatedly. In this flight test, the propellant mass flow estimated is mp=229 g/s. A time average thrust is Fave=254 N, the specific impulse of a propellant base is estimated to be Isp, PF =113 s, this specific impulse is 86 % of a ground test. The attitude of Todoroki incline to the positive direction of pitch up. The some factors of the inclination of Todoroki II are that the number of iginition different in each combustion tube and the attitude of Todoroki II launched is tilted. Considering these factors calculation results agree with experimental results in the attitude of Todoroki II.

In order to analyze a microwave neutralizer in ion’s time/space scales, a three-dimensional Hybrid-PIC (Particle-In-Cell) solver which treats ions and electrons as particles and fluid was developed. In this analysis, microwave power absorption distribution was estimated by means of another electromagnetic PIC solver. The results show that qualitative agreement on voltage-current characteristics was achieved, whereas a discontinuous current jump between a low current mode and a high current mode was still diffused. It is found that, in the high current mode, the electric potential is gradually increased toward the plume region inside the orifice, which promotes high ion production rate there. It is also shown that the sputtering rate of an antenna is comparable with the measured data, where doubly-ionized ions mainly produced inside the orifice considerably aggravate the sputtering rate.

Study of a Rotating Detonation Engine (RDE) has been carried out in many research institutions. The RDE has the advantage of high efficiency, simple structure and only once ignition. Toward the practical use for rocket engine, the evaluation of thrust efficiency and the knowledge of combustion under high acceleration or multiple degrees of freedom are essential. In this study, C2H4 + O2 mixture was used as propellant. A Slide mechanism for thrust measyrement was developed, and the mechanism reduced noise and exhausted burned gas. So, the thrust history was acquired and the thrust performance was assessed.

This paper investigated the quantitative current transport performance and thermal behaviour of a high temperature superconducting (HTS) coil, and the effect of the critical current inhomogeneity along the longitudinal direction of HTS tapes on the coil performances. We fabricated a double-pancake coil using a Bi-2223/Ag tape with a length of 200 m as a scale-down model for a magnetic sail spacecraft. We measured the current transport property and temperature rises during current applications of the HTS coil in a conduction-cooled system, and analytically reproduced the results on the basis of the percolation depinning model and three-dimensional heat balance equation. The percolation depinning model can describe the electric field versus current density of HTS tapes as a function of temperature and magnetic field vector, and we also introduced the longitudinal distribution of the local critical current of the HTS tape into this model. As a result, we can estimate the critical currents of the HTS coil within 10% error for a wide range of the operational temperatures from 45 to 80 K, and temperature rises on the coil during current applications. These results showed that our analysis and conduction-cooled system were successfully realized. The analysis also suggested that the critical current inhomogeneity along the length of the HTS tape deteriorated the current transport performance and thermal stability of the HTS coil. The present study contributes to the characterization of HTS coils and design of a coil system for the magnetic sail spacecraft. (C) 2013 Elsevier B. V. All rights reserved.

This study designed a high-temperature superconducting (HTS) coil using yttrium barium copper oxide (YBCO)-coated conductors, in order to obtain an adequate magnetic moment for a magnetic sail spacecraft. For the optimal design of the HTS coil system for use in space, we analyzed the current transport, thermal characteristics, and applied stresses of YBCO coils, on the basis of a magnetic field and thermal analysis, and the so-called percolation depinning model. After developing an analysis method, we designed an HTS coil to obtain a larger magnetic moment on the specific constraint conditions of a spacecraft system. As a result, we showed that a thin-walled coil with a large diameter (with outside diameter 4 m, number of layers 8 and stack number 512) can achieve a magnetomotive force at 2.0 x 10(6) A-turns and a larger magnetic moment with allowable stresses and high thermal stability for space missions. This study leads to the possibility of creating the world's first space propulsion system using an HTS coil.

The development of unique, high-density helicon plasma sources is described. Characterization of the largest and the smallest source sizes is made along with a discussion of particle production efficiency using Ar gas. Next, we describe an application of helicon sources to plasma propulsion using a new advanced concept without any eroding electrodes, as a review of our Helicon Electrodeless Advanced Thruster (HEAT) project.

The micro-Newton thrust generation was observed through low-power continuous wave laser and aluminum foil interaction without any remarkable ablation of the target surface. To evaluate the thrust characteristics, a torsion balance thrust stand capable for the measurement of the thrust level down to micro-Newton ranges was developed. In the case of an aluminum foil target with 12.5 micrometer thickness, the maximum thrust level was 15 micro-Newtons when the laser power was 20 W, or about 0.75 μN/W. It was also found that the laser intensity, or laser power per unit area, irradiated on the target was significantly important on the control of the thrust even under the low-intensity level. © 2012 Elsevier Ltd. All rights reserved.

Helicon sources are very effective in many aspects and are applicable in various science and technology fields, since they can supply high-density (∼ 1013 cm-3) plasmas with flexible operating parameters. In this paper, we characterize developed, featured sources in various sizes along with a discussion on a particle production efficiency. This activity was performed within the HEAT (Helicon Electrodeless Advanced Thruster) project aiming at development of the systems that can realize the schemes of completely electrodeless plasma production and acceleration. This is expected to mitigate a problem of finite life time inherent to electrodic plasma propulsion tools. Experimental and theoretical approaches to implementation of such the schemes are presented. © 2013 IEEE.

The plasma plume of a 1-MW-class quasi-steady magnetoplasmadynamic (MPD) arcjet is studied to determine the plume structure and plasma plume fluctuations in a downstream plume region (250-1250 mm away from the MPD arcjet). By using a double probe and a high-electron-temperature (similar to 5 eV) and high-number-density (similar to 8 x 10(19) m(-3)) region, so-called "cathode jets" are found along the central axis of plasma plume close to the MPD arcjet. Moreover, the plasma plume radial profile is constant in a downstream plume region (>= 750 mm from the MPD arcjet). The power spectrum density (PSD) of the ion saturation current is proportional to 1/f(1.6) (f: frequency) for f > 80 kHz, and in this frequency range, PSD decreased with distance from the MPD arcjet. In contrast, in the frequency region < 80 kHz, the PSD-f curve is at a constant value. Although a peak in the discharge voltage is attributed to the generalized lower hybrid drift instability (GLHDI), this instability is not found in the plasma plume near the MPD arcjet. The influence of the GLHDI is limited only to the discharge chamber, and fluctuations caused by the instability are random in the downstream region.

Under certain conditions during rocket flights, ionized exhaust plumes from solid rocket motors may interfere with radio frequency transmissions. To understand the relevant physical processes involved in this phenomenon and establish a prediction process for in-flight attenuation levels, we attempted to measure microwave attenuation caused by rocket exhaust plumes in a sea-level static firing test for a full-scale solid propellant rocket motor. The microwave attenuation level was calculated by a coupling simulation of the inviscid-frozen-flow computational fluid dynamics of an exhaust plume and detailed analysis of microwave transmissions by applying a frequency-dependent finite-difference time-domain method with the Drude dispersion model. The calculated microwave attenuation level agreed well with the experimental results, except in the case of interference downstream the Mach disk in the exhaust plume. It was concluded that the coupling estimation method based on the physics of the frozen plasma flow with Drude dispersion would be suitable for actual flight conditions, although the mixing and afterburning in the plume should be considered depending on the flow condition. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762857]

A discretization procedure for a total variation diminishing (TVD) scheme is introduced to an electromagnetic hybrid particle-in-cell (PIC) plasma simulation code in order to improve the numerical stability and resolution when calculating the plasma flow field in which magnetic field discontinuities (for example, Rankine-Hugoniot jump conditions for shock waves) are generated. In the hybrid PIC code used in this study, ions are treated as particles and electrons are assumed to be an inertia-less (mass-less) fluid. In the numerical results of one-dimensional test simulations, the TVD scheme significantly prevents non-physical, numerical oscillations, which would ordinarily be produced in the solution when the convection term of the magnetic induction equation in the hybrid PIC code is discretized by central difference schemes at magnetic field discontinuities. Furthermore, a two-dimensional simulation of the global structure of a collision-less bow shock, which is suitable for practical use, makes it possible to clearly capture the bow shock by using the hybrid PIC code with the TVD scheme. (C) 2012 Elsevier B.V. All rights reserved.

Full penetration of RF electric fields into magnetized plasmas is expected in order to realize the Lissajous helicon plasma accelerator (LHPA). We study the electric field penetration in bulk plasma in one-dimensional electrostatic approximation using two analytical models: the matrix sheath model and the vacuum gap model. An identical formula for the electric field is obtained from the models. The formula is benchmarked by particle-in-cell (PIC) simulations. The full penetration of the electric field is realized when the relation (q &lt;&lt; 0.01) is satisfied, where q is the measure of the degree of the shielding effect due to plasma density and electron magnetization. (C) 2012 The Japan Society of Applied Physics

Performance of a repetitively pulsed self-field MPD thruster consisting of a flared anode and a short cathode was numerically investigated. For a time-averaged input power of 100 kW and argon propellant, thrust and thrust efficiency were surveyed for various discharge frequencies under the condition of continuous propellant injection and a constant discharge duty ratio of 0.5. The results suggest that thrust efficiency of repetitively pulsed discharge operation can be improved up to about 16% with increasing discharge frequency owing to a relatively high time-averaged electromagnetic thrust and an increase in aerodynamic thrust, and can surpass that of continuous discharge operation above 50 kHz. It is also shown that the frozen flow loss can be reduced by increasing discharge frequency, because the input power needed for reionization of the propellant can be suppressed. (C) 2012 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

A magnetic sail generates a propulsive force using the interaction between the solar wind and an artificial magnetosphere generated by a hoop coil. To investigate the electromagnetic thrust characteristics of the magnetic sail, such as the values of the drag, lift, transverse force, and pitching moment, three-dimensional hybrid (ion particle and electron fluid) particle-in-cell simulations are conducted in the range from the ion inertial scale to the magnetohydrodynamic scale. The drag values calculated in the different magnetic moment directions to the solar wind flow direction agree to within a factor of 2. The attitude of spacecraft is stable when the magnetic moment vector is perpendicular to the solar wind flow direction. It is found that these two results do not depend on the size of the magnetosphere.

The magnetic sail is an advanced space propulsion concept that uses an artificial magnetosphere for capturing the solar wind energy. In this study, the interaction of the solar wind with the magnetosphere of a magnetic sail has been simulated based on the resistive magnetohydrodynamics model in two-dimensional space and the plasmadynamic characteristics of magnetic sail were evaluated. When the solar wind is not magnetized by the interplanetary magnetic field, the attitude of the magnetic sail spacecraft is static stable when the magnetic moment vector is perpendicular to the solar wind flow direction. The interplanetary magnetic field not only enhances a drag force in the direction leaving the sun (i.e., thrust) but also acts on the pitching moment; the pitching moment due to the interplanetary magnetic field rotates the magnetic sail spacecraft so as to align the magnetic moment vector parallel to the interplanetary magnetic field. Despite the weak interplanetary magnetic field adopted in the simulation, which is I order of magnitude lower, than the typical value, the pitching moment coefficient is significant. The attitude stability of the magnetic sail is hence strongly affected by the interplanetary magnetic field.

The magnetic sail is a spacecraft propulsion system that uses the interaction between the magnetic field and the solar wind. In this paper, to evaluate the thrust characteristics of a magnetic sail spacecraft, a new numerical model, including the ion's finite Larmor-radius effect, is proposed. In this model, the trajectories of ion particles are solved based on a flux-tube model, and electrons are treated as a plasma fluid under the assumption of quasineutrality and a steady state. As for the electromagnetic field, the induction equation is employed to obtain the electrostatic field and the static magnetic field. Using the new model, a 500 km magnetosphere was found to produce a thrust level of 1500 N when the magnetic moment of the magnetic sail (3.9 x 10(16) Wbm) is parallel to the solar wind. This thrust level agrees well with results obtained by the rnagnetohydrodynamics model (1600 N) and by the hybrid particle-in-cell (PIC) model, including the ion kinetic effects (1560 N). Also, the computational cost of the new flux-tube model is reduced to about 1/10 of that of the hybrid-PIC model.