Cross-scale coupling at a perpendicular collisionless shock
aa r X i v : . [ phy s i c s . p l a s m - ph ] A p r Cross-scale coupling at a perpendicular collisionless shock
Takayuki Umeda, Masahiro Yamao
Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya 464-8601, JAPAN
Ryo Yamazaki
Department of Physical Science, Hiroshima University, Higashi-Hiroshima 739-8526, JAPANPresent address: Department of Physics and Mathematics, Aoyama Gakuin University, 5–10–1, Fuchinobe, Sagamihara,Kanagawa, 252-5258, JAPAN
Abstract
A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Machnumber ( M A = 5). Recent self-consistent hybrid and full particle simulations have demonstrated ion kinetics areessential for the non-stationarity of perpendicular collisionless shocks, which means that physical processes due to ionkinetics modify the shock jump condition for fluid plasmas. This is a cross-scale coupling between fluid dynamics andion kinetics. On the other hand, it is not easy to study cross-scale coupling of electron kinetics with ion kinetics orfluid dynamics, because it is a heavy task to conduct large-scale full particle simulations of collisionless shocks. In thepresent study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a “shock-rest-frame model”. The simulation domain is taken to be larger than the ion inertial length in order to include full kineticsof both electrons and ions. The present simulation result has confirmed the transition of shock structures from thecyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions are thermalizedin the direction parallel to the shock magnetic field. Ions are thermalized by low-frequency electromagnetic waves (orrippled structures) excited by strong ion temperature anisotropy at the shock foot, while electrons are thermalizedby high-frequency electromagnetic waves (or whistler mode waves) excited by electron temperature anisotropy at theshock overshoot. Ion acoustic waves are also excited at the shock overshoot where the electron parallel temperaturebecomes higher than the ion parallel temperature. We expect that ion acoustic waves are responsible for paralleldiffusion of both electrons and ions, and that a cross-scale coupling between an ion-scale mesoscopic instability and anelectron-scale microscopic instability is important for structures and dynamics of a collisionless perpendicular shock. Key words: collisionless shock; particle-in-cell simulation; cross-scale coupling
1. Introduction
Dynamics of shock waves in plasmas are oftendiscussed by the shock jump conditions (Rankine-Hugoniot conditions), which describe conservationlaws of mass, momentum, energy, normal magneticfield and motional electric field for fluid plasmas.
Email address: [email protected] (TakayukiUmeda).
On the other hand, previous kinetic simulationsrevealed that collisionless shocks in plasmas can bestrongly non-stationary in both spatial and tem-poral scales of ions. In the direction normal to theshock surface of a quasi-perpendicular collision-less shock, a new shock front periodically appears(e.g., Biskamp and Welter, 1972; Quest, 1985; Lem-bege and Dawson, 1987; Lembege and Savoini,1992; Hellinger et al., 2002), which is called theself-reformation. Incoming ions are reflected up-
Article to be published in Planetary and Space Science 2 November 2018 tream at the shock ramp of a supercritical quasi-perpendicular collisionless shock, and they form afoot in front of the ramp during their gyration. Atthe upstream edge of the foot, ions are accumu-lated in time and are reflected upstream, which areresponsible for the self-reformation. The cyclic self-reformation is due to ion dynamics, although thisprocess has been confirmed in both electromagnetichybrid and full particle simulations. In addition,recent full particle simulations have shown thatelectron-scale micro instabilities, such as Bunemaninstability (e.g., Shimada and Hoshino, 2000) andmodified two-stream instability (e.g., Scholer etal., 2003) are excited at the foot during the cyclicself-reformation. Scholer and Matsukiyo (2004) hasalso demonstrated that the modified two-stream in-stability is also responsible for the self-reformation.Another mechanism of the self-reformation is steep-ening of whistler mode waves in upstream regionsof oblique shocks (Krasnoselskikh et al., 2002).In the shock-tangential direction, on the otherhand, there appear fluctuations in the spatial scaleof ion inertial length in the direction parallel tothe shock magnetic field (Winske and Quest, 1988;Lowe and Burgess, 2003) or ion gyro radius of re-flected ions in the direction perpendicular to theshock magnetic field (Burgess and Scholer, 2007),which are called the “ripples”. The compression ofincoming ions at collisionless shocks results in theiradiabatic heating in the shock-normal direction. Inquasi-perpendicular shocks, however, the ion heat-ing in the shock-normal direction is more dominatedby the gyration of reflected ions. Thus an ion temper-ature anisotropy between shock-normal and shock-tangential directions becomes a common feature inthe transition region of quasi-perpendicular shocks.The dynamic rippled character of the shock sur-face is thought to be related to the ion tempera-ture anisotropy. Although this process has been con-firmed in two-dimensional (2D) electromagnetic hy-brid particle simulations, it is difficult to take intoaccount the dynamic rippled character of the shocksurface in 2D electromagnetic full particle simula-tions. This is because current computer resourcesare not necessarily enough to take such a large sim-ulation domain of several ion inertial length.Very recently, however, there are several attemptsof 2D electromagnetic full particle simulations thattake into account ion dynamics in both shock-normal and shock-surface directions (Hellinger etal. 2007; Amano and Hoshino, 2009; Lembege etal., 2009). These results indicate that ion-scale fluc- tuations at perpendicular collisionless shocks candynamically change electron-scale processes such aswave excitation and electron acceleration. The pur-pose of this paper is to examine a cross-scale cou-pling between the dynamic rippled character of theshock surface and electron-scale micro instabilities.In order to take into account ion dynamics in bothshock-normal and shock-surface directions, a large-scale 2D electromagnetic full particle simulation iscarried out by using the “shock-rest-frame model”.
2. Full Particle Simulations
Shock-Rest-Frame Model
There are several different methods for excitingcollisionless shocks in kinetic simulations of plas-mas. These include the injection method (or thereflection/wall method) (e.g., Quest, 1985; Winskeand Quest, 1988; Shimada and Hoshino, 2000;Hellinger et al. 2002; Lowe and Burgess, 2003;Scholer et al., 2003; Burgess and Scholer, 2007;Amano and Hoshino, 2009). the plasma releasemethod (Ohsawa, 1985), and the magnetic pistonmethod (e.g., Biskamp and Welter, 1972; Lembegeand Dawson, 1987; Lembege and Savoini, 1992). Inthese methods, collisionless shocks are excited by aninteraction between a supersonic plasma flow anda resting plasma. The simulation domain is takenin the downstream rest frame with the injectionmethod, while the simulation domain is taken inthe upstream rest frame withe the plasma releaseand magnetic piston methods. Thus an excitedshock wave propagates upstream in these methods.There is also another method called the flow-flowmethod for exciting collisionless shocks (e.g., Omidiand Winske, 1992). Since collisionless shocks areexcited by an interaction between two supersonicplasma flows in this method, there exist forwardand reverse shock waves. A big problem in thesemethods is that excited collisionless shock wavespropagate at a fast velocity, and it is necessary totake a very long simulation domain in the propaga-tion direction of the shock waves in order to follow along-time evolution of the shock waves. This makesit difficult to perform multidimensional simulationseven with current supercomputer systems.An alternative is to excite collisionless shocks inthe shock rest frame with the “relaxation method”,whereby collisionless shocks are excited by an inter-action between a supersonic plasma flow and a sub-2onic plasma flow moving in the same direction. Thismethod was first used in hybrid particle simulationsin 1980’s (e.g., Leroy et al., 1981, 1982), and thenin full particle simulations in 1990’s (Pantellini etal., 1992; Krauss-Varban et al., 1995). This methodwas not so popular because of several difficulties innumerical techniques, and its application to long-term evolution of shock waves was not considered.In 2000’s, however, long-term 1D simulations withthe relaxation method have been performed by us-ing Darwin particle code (Muschietti and Lembege,2006) and full electromagnetic particle code (Umedaand Yamazaki, 2006). Very recently, the relaxationmethod has also been applied to long-term 2D fullelectromagnetic particle simulations (Umeda et al.,2008, 2009). In general, it is not easy to perform alarge-scale (ion-scale) multidimensional full electro-magnetic particle simulations of collisionless shockseven with present-day supercomputers. Hence theshock-rest-frame model is important to be able tofollow the evolution of shock waves for a long termwith a limited computer resource.2.2.
Simulation Setup
We use a 2D full electromagnetic particle code(Umeda, 2004), in which the full set of Maxwell’sequations and the relativistic equation of motionfor individual electrons and ions are solved in aself-consistent mannar. The continuity equation forcharge is also solved to compute the exact currentdensity given by the motion of charged particles(Umeda et al., 2003).The initial state consists of two uniform regionsseparated by a discontinuity. In the upstream re-gion that is taken in the left hand side of the sim-ulation domain, electrons and ions are distributeduniformly in space and are given random velocities( v x , v y , v z ) to approximate shifted Maxwellian mo-mentum distributions with the drift velocity u x ,number density n ≡ ǫ m e ω pe /e , isotropic tem-peratures T e ≡ m e v te and T i ≡ m i v ti , where m , e , ω p and v t are the mass, charge, plasma frequencyand thermal velocity, respectively. Subscripts “1”and “2” denote “upstream” and “downstream”,respectively. The upstream magnetic field B y ≡− m e ω ce /e is also assumed to be uniform, where ω c is the cyclotron frequency (with sign included).The downstream region taken in the right-handside of the simulation domain is prepared similarlywith the drift velocity u x , density n , isotropic temperatures T e and T i , and magnetic field B y .We take the simulation domain in the x - y planeand assume a perpendicular shock (i.e., B x = 0).Since the ambient magnetic field is taken in the y direction, free motion of particles along the ambientmagnetic field is taken into account. As a motionalelectric field, a uniform external electric field E z = − u x B y = − u x B y is applied in both upstreamand downstream regions, so that both electrons andions drift in the x direction. At the left boundaryof the simulation domain in the x direction, we in-ject plasmas with the same quantities as those inthe upstream region, while plasmas with the samequantities as those in the downstream region arealso injected from the right boundary in the x direc-tion. We adopted absorbing boundaries to suppressnon-physical reflection of electromagnetic waves atboth ends of simulation domain in the x direction(Umeda et al., 2001), while the periodic boundariesare imposed in the y direction.In the relaxation method, the initial conditionis given by solving the shock jump conditions(Rankine-Hugoniot conditions) for a magnetizedtwo-fluid isotropic plasma consisting of electronsand ions (Hudson, 1970). In order to determine aunique initial downstream state, we need given up-stream quantities u x , ω pe , ω ce , v te , and v ti andan additional parameter. We assume a low-betaand weakly-magnetized plasma such that β e = β i = 0 .
125 and ω ce /ω pe = − . m i /m e = 25 for computational efficiency. Thelight speed c/v te = 40 . u x /v te = 4 . M A = ( u x /c ) | ω pe /ω ce | p m i /m e = 5 .
0. Theion-to-electron temperature ratio in the upstreamregion is given as T i /T e = 1 .
0. In this study, down-stream ion-to-electron temperature ratio T i /T e =8 . ω pe /ω pe =1 . ω ce /ω pe = 0 . u x /v te = 1 . v te /v te = 2 . N x × N y =2048 × N x × N y = 2048 × x/λ De = 1 . ω pe ∆ t = 0 . λ De is theelectron Debye length upstream. Thus the total size3f the simulation domain is 10 . l i × . l i which islong enough to include the ion-scale rippled struc-ture, where l i = c/ω pi (= 200 λ De ) is the ion iner-tial length. In Run B, we use N x × N y = 2048 × N x × N y = 2048 ×
128 cells for the downstream region, respectively.Thus the the total size of the simulation domain is10 . l i × . l i , in which ion-scale processes alongthe ambient magnetic field is neglected. We used 16pairs of electrons and ions per cell in the upstreamregion and 64 pairs of electrons and ions per cell inthe downstream region, respectively, at the initialstate.
3. Results
Figure 1 shows the tangential component ofmagnetic field B y as a function of position x andtime t for Runs A and B. The position and timeare renormalized by the ion inertial length l i andthe ion cyclotron angular period 1 /ω ci , respec-tively. The magnitude is normalized by the initialupstream magnetic field B y . In Fig.1, the tan-gential magnetic fields B y are averaged over the y direction, which means that fluctuations in theshock-tangential direction are neglected.In the present shock-rest-frame model, a shockwave is excited by the relaxation of the two plas-mas with different quantities. Since the initial stateis given by the shock jump conditions for a “two-fluid” plasma consisting of electrons and ions, thekinetic effect is excluded in the initial state and theexcited shock becomes “almost” at rest in the simu-lation domain. In both runs, the shock front appearsand disappears on a timescale of the downstreamion gyro period, which corresponds to the cyclic self-reformation of a perpendicular shock. The reforma-tion takes place for more than ω ci t = 12 in Run B,while the reformation seems to be less significant af-ter ω ci t ∼ ω ci t ∼ Fig. 1. Tangential magnetic field B y as a function of position x and time t for Runs A and B. The position and time arenormalized by λ i and 1 /ω ci , respectively. The magnitudeis normalized by the initial upstream magnetic field B y .The magnetic fields are averaged over the y direction. the shock surface (ripples) do not appear and theprofiles of electromagnetic fields become almostone-dimensional (Umeda et al., 2008, 2009), andthere exists apparent cyclic self-reformation of theperpendicular shock as seen in Run B. The presentresult suggests that the ion-scale fluctuations in theshock-tangential direction play an important rolein the sequential appearance of non-stationary andquasi-stationary shock fronts.Figure 2 shows the electron and ion temperaturesas a function of position x and time t for Run A.The panels (a), (b) and (c) corresponds to the tem-perature ratios T e || /T i || , T i || /T i ⊥ and T e || /T e ⊥ , re-spectively. The panels (d) and (e) corresponds to theparallel temperatures of electrons and ions, T e || and T i || , respectively. Note that these temperatures areaveraged over the y direction, and that the paral-lel temperatures are approximated by the tempera-tures in the y direction while the perpendicular tem-peratures are approximated by the average of tem-peratures in the x and z directions.From ω ci t ∼
7, the electron temperature in the4 ig. 2. Electron and ion temperatures as a function of position x and time t for Run A. (a) T e || /T i || , (b) T i || /T i ⊥ , (c) T e || /T e ⊥ ,(d) T e || , and (e) T i || . The position and time are normalized by λ i and 1 /ω ci , respectively. The temperatures are normalizedby the initial upstream temperature ( T e = T i ). These temperatures are averaged over the y direction. Here, the paralleltemperatures are approximated by the temperatures in the y direction while the perpendicular temperatures are approximatedby the average of temperatures in the x and z directions. direction parallel to the ambient magnetic field, T e || ,at the shock overshoot becomes twice as large as theion parallel temperature, T i || . At the shock foot, theelectron perpendicular temperature, T e ⊥ , is higherthan the electron parallel temperature, T e || . On theother hand, T e || becomes higher than T e ⊥ at theshock overshoot. In the downstream region, T e || isslightly higher than T e ⊥ . As seen in Fig.2d, electronsare strongly thermalized in the direction parallel tothe shock magnetic field at the overshoot, suggestingthat there exists a strong parallel diffusion process atthe overshoot from ω ci t ∼
7. On the other hand, ionparallel temperature becomes higher at the shockfoot and in the downstream region as seen in Fig.2e.Fig.2 shows that electrons and ions are thermalizedin different regions, suggesting that electrons andions heating takes place on different scales.Figure 3 shows snapshots of shock magnetic field B y , ion density n i , ion parallel temperature T i || , ionparallel temperature T i ⊥ , and ion temperature ra-tio T i || /T i ⊥ . at ω ci t = 12 for Runs A and B. Al-though the Mach number of the present simulationrun is relatively low ( M A = 5), the present perpen-dicular shock is supercritical, and therefore the cy-clotron motion of reflected ions is dominant for ionheating in the shock-normal direction. At the shockovershoot, the ion parallel and perpendicular tem-peratures are low because of the accumulation ofupstream cold ions. The ion perpendicular temper-ature becomes higher at the shock foot because ofthe non-gyrotropic velocity distribution of reflectedions. At the shock foot, ions are also thermalized in the parallel direction because of an anisotropy-driven ion cyclotron wave in Run A. However, theion parallel heating is not responsible for the elec-tron parallel heating (see Fig.2). As seen in Fig.3,the ion temperature anisotropy ( T i ⊥ /T i || >
1) wouldbe a common feature at perpendicular collisionlessshocks. In Run B, there is no ion parallel heatingbecause the system length does not allow the ex-istence of an ion cyclotron wave in the parallel di-rection. Thus the temperature anisotropy becomesmuch higher than in Run A.In order to study mechanisms for parallel heat-ing of electrons and ions, we take Fourier transfor-mation of the shock-normal magnetic field compo-nent B x and the shock-tangential electric field com-ponent E y in the transition region. Figure 4 showsfrequency-wavenumber spectra of the shock-normalmagnetic field component B x for different time inter-vals: (a) ω ci t = 4 ∼
6, (b) ω ci t = 6 ∼
8, (c) ω ci t =8 ∼
10, and (d) ω ci t = 10 ∼
12. The frequency andwavenumber are normalized by ω pe and ω pe /v te ,respectively. These frequency-wavenumber spectraare obtained by projection of ω − k x − k y spectraonto the ω − k y plane. Note that the typical electronand ion cyclotron frequencies in the transition re-gion are ω ce ∼ . ω pe and ω ci ∼ . ω pe , respec-tively, and their maximum values are ω ce ∼ . ω pe and ω ci ∼ . ω pe , respectively, at the overshoot.In Fig.4, we found a strong enhancement of B x component below ω ci , which might correspond tothe rippled structures due to the ion temperatureanisotropy. We also found an enhancement of B x ig. 3. Spatial profiles of shock magnetic field B y , ion density n i , ion parallel temperature T i || , ion parallel temperature T i ⊥ , and ion temperature ratio T i || /T i ⊥ . at ω ci t = 12 forRuns A and B. component over ω ci , suggesting that electromag-netic electron cyclotron waves are excited in thetransition region, which might correspond to the“nonlinear whistler waves” reported by Hellinger etal. (2007) and Lembege et al. (2009).For ω ci t = 6 ∼ ω/ω pe = 0 .
4, while other time intervals the B x com-ponent is enhanced up to ω/ω pe = 0 .
4, implyingthat the high-frequency waves are responsible for theparallel heating of electrons at ω ci t ∼ ω ci t >
7, whistler mode waves due to electron temperatureanisotropy.Ions are thermalized in the direction parallel tothe shock magnetic field by the low-frequency elec-tromagnetic waves below ω ci . However, these wavesare not so much responsible for the parallel heatingof electrons, because there is not significant paral-lel heating of electrons at the shock foot as seen inFig.2d.Figure 5 shows frequency-wavenumber spectraof the shock-normal magnetic field component E y in the transition region for different time intervals:(a) ω ci t = 4 ∼
6, (b) ω ci t = 6 ∼
8, (c) ω ci t =8 ∼
10, and (d) ω ci t = 10 ∼
12. with the sameformat as Fig.4. The typical ion plasma frequencyin the transition region is ω pi ∼ . ω pe , and itsmaximum value is ω ce ∼ . ω pe at the overshoot.For ω ci t = 6 ∼
12, we found a strong enhance-ment of the E y component up to ω/ω pe ∼ .
7, whilethere is not any enhancement in a high-frequencyrange for ω ci t = 4 ∼
6. The phase velocity of thesewave are estimated as v p /v te = 1 . ∼ .
5. FromFig.2, the typical parallel temperatures of electronsand ions are estimated as T e || ∼ T e and T e || ∼ T i . Thus the ion acoustic velocity is obtained as v s = s T e || + γT i || m i ∼ . v te (1)with γ = 3, suggesting that the ion acoustic wavesare excited in the transition region. As shown inFig.2a, the electron parallel temperature becomeshigher than the ion parallel temperature due to elec-tron cyclotron waves at the shock overshoot, whichis a suitable condition for excitation of ion acoustic6 ig. 4. Frequency-wavenumber spectra of the shock-nor-mal magnetic field component B x for different time in-tervals in Run A. (a) ω ci t = 4 ∼
6, (b) ω ci t = 6 ∼ ω ci t = 8 ∼
10, and (d) ω ci t = 10 ∼
12. TheFourier transformation is taken for y/l i = 0 ∼ .
12, (a) x/l i = − . ∼ .
5, (b)-(d) x/l i = − . ∼ .
0. These fre-quency-wavenumber spectra are obtained by projection of ω − k x − k y spectra onto the ω − k y plain. The frequencyand wavenumber are normalized by ω pe and 1 /λ De , re-spectively. The magnitude is normalized by the upstreammagnetic field B y . Fig. 5. Frequency-wavenumber spectra of the shock-normalmagnetic field component E y for different time intervals inRun A, with the same format as Fig.4. (a) ω ci t = 4 ∼ ω ci t = 6 ∼
8, (c) ω ci t = 8 ∼
10, and (d) ω ci t = 10 ∼ E z . y direction. The shock front becomes turbulent in-stead of quasi-stationary. We expect that the ionacoustic waves would play a role in the transitionprocess from the self-reformation phase to the tur-bulent phase, because ion acoustic waves are respon-sible for diffusion of both electrons and ions along amagnetic field.
4. Summary
We performed a 2D electromagnetic full particlesimulation of a low-Mach-number perpendicular col-lisionless shock. The results are itemized below.(i) It has been confirmed that the cyclic self-reformation of the shock front becomes lesssignificant as time elapses, which is consistentwith the previous 2D simulations (Hellingeret al., 2007; Lembege et al., 2009). The shockfront appears to be “quasi-stationary” byaveraging the spatial profiles of electromag-netic fields over the shock-tangential direc-tion, although electron-scale microscopic andion-scale mesoscopic instabilities are quite dy-namic and the shock front becomes turbulent.(ii) During the transition from the cyclic self-reformation to the turbulent shock front,electrons and ions are thermalized in the di-rection parallel to the shock magnetic field indifferent regions and by different mechanisms.The electron parallel temperature is more en-hanced than the parallel ion temperature atthe shock overshoot.(iii) Low-frequency electromagnetic (ion cyclotronor mirror mode) waves are excited at the shockfoot, which corresponds to the rippled struc-ture in the shock-tangential direction. Thesewaves are excited by the strong temperatureanisotropy of ions. Ions are thermalized in thedirection parallel to the shock magnetic fieldby these waves, but electrons are not.(iv) Electromagnetic electron cyclotron (whistlermode) waves are excited at the shock over-shoot. These waves are excited by the tem-perature anisotropy of electrons. Electrons arethermalized in the direction parallel to theshock magnetic field by these waves, but ionsare not. (v) Strong parallel heating of electrons at theshock overshoot results in the suitable condi-tion for excitation of ion acoustic waves. Therippled structure might be an energy sourceof the ion acoustic waves. However, their de-tailed excitation mechanism is not yet clear.The ion acoustic waves are responsible forparallel diffusion of both electrons and ions.We expect that the ion acoustic waves have adirect implication with the transition from theself-reformation phase to the turbulent phase.(vi) A cross-scale coupling between an ion-scalemesoscopic instability and an electron-scalemicroscopic instability is important for struc-tures and dynamics of collisionless perpendic-ular shocks. Hence large-scale full kinetic sim-ulations are quite important.It is noted that Yuan et al. (2009) have demon-strated the cyclic self-reformation in their 2D hy-brid simulation of a quasi-perpendicular shock with θ = 85 ◦ , which is different from the results in purelyperpendicular shocks. We are now trying to checkwhether the reformation is suppressed or not at aoblique shock by a large-scale 2D PIC simulation.However, this is beyond the scope of the present pa-per.Finally, the effect of mass ratio is discussed.In the present simulation parameter ( M A =5 , ω pe /ω ce = 10 , β = 0 . m i /m e = 1836, the thermalvelocity of upstream electrons becomes about 8.6times as large as the case of m i /m e = 25, and theelectron cyclotron modes are stabilized. In contrastwith current driven instability, obliquely propagat-ing whistler mode waves becomes unstable due tomodified two-stream instability (Matsukiyo and Sc-holer, 2003, 2006). However, the evolution of modi-fied two-stream instability at perpendicular shockshas been studied only in a localized uniform model(Matsukiyo and Scholer, 2006). The influences ofmodified two-stream instability on the reformationprocess of perpendicular shocks is an outstandingissue to be addressed by future 2D PIC simulationsof perpendicular collisionless shocks.8 cknowledgements The authors are grateful to S. Matsukiyo and Y.Ohira for discussions. The computer simulationswere carried out on Fujitsu HPC2500 at ITC inNagoya Univ. and NEC SX-7 at YITP in KyotoUniv. as a collaborative computational researchproject at STEL in Nagoya Univ. and YITP inKyoto Univ. This work was supported by Grant-in-Aid for Scientific Research on Innovative AreasNo.21200050 (T. U.), Grant-in-Aid for Scientific Re-search on Priority Areas No.19047004 (R. Y.) andGrant-in-Aid for Young Scientists (B) No.21740184(R. Y.) from MEXT of Japan.
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