Experimental observation of the transport induced by ion Bernstein waves near the separatrix of magnetic nulls

Renchuan HE(何任川),Xiaoyi YANG(楊肖易),,Chijie XIAO(肖池階),*,Xiaogang WANG(王曉鋼),Tianchao XU(徐田超),*,Zhibin GUO(郭志彬),Yue GE(蓋躍),Xiuming YU(余修銘),Zuyu ZHANG(張祖煜),Rui KE(柯銳) and Ruixin YUAN(袁瑞鑫)

1 State Key Laboratory of Nuclear Physics and Technology,School of Physics,Peking University,Beijing 100871,People’s Republic of China

2 Department of Physics,Harbin Institute of Technology,Harbin 150001,People’s Republic of China

3 Center for Fusion Science of Southwestern Institute of Physics,Chengdu 610041,People’s Republic of China

Abstract The waves in a magnetic null could play important roles during 3D magnetic reconnection.Some preliminary clues in this paper show that the ion Bernstein wave(IBW)may be closely related to transport process in magnetic null region.The magnetic null configuration experiment reported here is set up in a linear helicon plasma device,Peking University plasma test device(PPT).The wave modes with frequencies between the first and third harmonics of local ion cyclotron frequency(ωci)are observed in the separatrix of magnetic null,which are identified as the IBW based on the dispersion relation.Further analysis shows that IBW could drive substantial particle flux across the magnetic separatrix.The theoretical radial particle flux driven by IBW and the measured parallel flow in PPT device are almost on the same order,which shows that IBW may play an important role during 3D reconnection process.

Keywords:separatrix,ion Bernstein wave,particle transport,magnetic null,magnetic reconnection

1.Introduction

Magnetic reconnection is an important issue in plasma physics,which is often accompanied by fast change and reconfiguration of different magnetic topology,and quick conversion between the plasma kinetic energy,thermal energy and magnetic field energy.Most studies focus on the relations between the plasma waves and reconnection trigger process,reconnection rate,energy conversion,etc[1,2].A lot of waves have been observed in reconnection region,such as the Alfvén wave,whistler wave,low hybrid wave,etc[3,4].Those waves propagate almost parallel to the magnetic field lines.To study the physical process perpendicular to the reconnection plane,even the typical spatial scales,the perpendicular modes need to be taken into account,e.g.some drift waves have been mentioned[5,6].Recently,the ion Bernstein wave(IBW)has been observed in a magnetic reconnection region in the Earth’s magnetotail[7].

The magnetic separatrix is the boundary of different magnetic topological regions which widely exists in the solar surface,the Earth’s magnetosphere,the tokamak plasma,etc.The particle transport and energy transport across the separatrix play important roles in various magnetic configurations[1,8],e.g.the non-null reconnection could happen in the separatrix region in 3D magnetic-nulls configurations.Also,the particle transport in the scrape-off layer(SOL)region shows substantial influence on tokamak plasma confinement[9].

In order to study the particle transport,as well as the perpendicular-propagating waves near the separatrix of magnetic nulls,we set up a stationary magnetic-null configuration in the plasma test device(PPT)device.Here we report that the IBW[10]is observed near the separatrix in the experiment.The particle flux induced by the IBW has also been found,which is confirmed to be much stronger than the flux driven by other wave modes.

This paper is organized as follows.The first part goes to the introduction.The experiment method of our research,including both the experiment setup and the probe diagnosis,is introduced in section 2.Some preliminary results of IBW experiments are presented in section 3.The particle transport driven by the IBW across the separatrices of magnetic nulls is shown in section 4.Then conclusion and discussions are listed in the last section.

2.Experiment method

The PPT device has a cylindrical vacuum chamber with a 250 mm radius and an overall length of 1000 mm.0-2000 G uniform magnetic field is generated by a pair of Helmholtz coils[11,12].A dipole magnetic field is constructed by placing a hollow cylinder permanent magnet with an 88 mm inside diameter,a 152 mm outer diameter and 140 mm length on the central axis.The distance from center to the separatrices(white line circle in figure 1(a))of magnetic nulls could vary from 90 to 130 mm,which is adjusted by the external magnetic field,from 260 to 660 G,provided by Helmholtz coils.A 13.56 MHz helicon plasma source is used to generate plasma of density up to 1×1012cm-3with an argon gas pressure of about 2 mTorr.The power of the helicon source is set within the range from 1000 to 2000 W for a stable discharge.In the experiment reported in this paper,the asymptotic magnetic field is 395 G and the helicon discharge power is 1500 W as shown in figure 1(a).

The probe diagnosis system is set in a port(red circle in figure 1(c))in the center of electromagnet coils.Plasma parameters are obtained from the Langmuir probes with a 10 mm s-1scan velocity and recorded in NI 6368 Data Acquisition with sampling frequency up to 2 MHz.

Measurements of plasma density and floating potential profiles are made by two horizontal 9-tip probe arrays.One array measures floating potential(Uf)and the other one measures ion-saturation current(Isat),biased by-49 V.Each tungsten tip is 1 mm in diameter,1 mm in length and in a ceramic tube with a diameter of 2.4 mm.The distances between adjacent tips are 3 mm.Figure 1(b)shows the photo of the 9-tip probe arrays in helicon plasma.

Figure 1.Schematic diagram of the magnetic field for the experiments in this paper.(a)The diagram of a magnetic null configuration,and the nine-probe array in the helicon plasma of PPT device.(b)During the experiment nine-tip probe array was extended into the separatrix.(c)The diagram of the PKU plasma test device(PPT).Helical wave plasma is generated through the RF antenna.A Helmholtz coil provides a uniform magnetic field in the middle of the device,while the probe extends through the probe window via a motorized probe platform.After placing a permanent magnet in the center of the device,our experimental configuration was constructed.

Figure 2.The ion density and floating potential profiles.(a)Ion density profile.(b)Floating potential profile.The five red dotted lines represent the radial range of phase profiles in figure 4.

Various physical quantities are measured simultaneously by a 5-tip probe array,in which one tip measuresIsatand the other four measureUf.TheIsattip is located in the center of the cross placement 5-tip probe,and the distances between adjacent tips are 3 mm.Two tips measuringUfof equal length to the tip measuringIsatare placed below and above theIsattip.The other twoUftips are 1 mm longer and 1 mm shorter than theIsattip.Details about the layout of the 5-tip probe array can be found in[12].Here we assume the electron temperature fluctuation is negligible as described in[13].Therefore,the fluctuating plasma potential is approximately equal to the fluctuating floating potential,which means the 5-tip probe array could measure plasma density(ni),floating potential(Uf),radial electric field(Er)and poloidal electric field(Ep).

Measurement of plasma velocity is made by Mach probe based on the pre-sheath theory[14,15],which is composed of two tips measuringIsatand a ceramic plate between the tips.

3.IBW on separatrix

In the case we reported here,the plasma ion density is about 1018m-3and the electron temperature is about 3 eV.The ion acoustic velocity calculated byis about5 km s-1and the Alfvén speed respectively calculated byis about 102km s-1,in which‘B’stands for local magnetic induction intensity.

Figures 2(a)and(b)show the ion density and floating potential profiles.The abscissa in figure 2 is axial position along thez-axis in figure 1,and the ordinate is the radial position along they-axis in figure 1 in mm.The position of the separatrix is estimated by the magnetic distribution as shown in figure 1.The magnetic field line is visible in figure 2 because the potential on the same magnetic line is almost equal.Potential well and ion density maximum are observed clearly near the separatrix where the electric field and density gradient may induce plasma waves or instabilities.

The auto-spectra of floating potential(figure 3(a))and plasma density(figure 3(b))show the perturbation modes with maximum amplitude near the separatrix located at 30 kHz,38 kHz,between the first and third harmonic ion cyclotron frequency in the 450 G magnetic field measured by Hall effect Gauss meter at=r 104 mm.In figures 3(a)-(c),the abscissa is the radial position in mm,and the ordinate is the frequency in kHz.The magnetic fluctuations amplitude is about 0.01 G forω=30 kHz in our experiment,which is diagnosed by magnetic probes.The amplitude of the electromagnetic component of this wave is calculated bywhich is less than3 V m-1,and the maximum value of electrostatic disturbance measured by the 5-tip probe is100 V m-1.Therefore,the magnetic component of IBW in the experiment should be much smaller than the electrostatic component based on the above experimental results.Therefore,the wave is identified as quasi-electrostatic wave mode in the separatrix region.

The dispersion relation of waves in the separatrix region is indicated in figure 3(d).The poloidal wave numberkis shown as the abscissa incm-1and the frequency is shown as the ordinate.The dispersion relationship betweenθk and f is calculated using two equal length tips of the 5-tip probe,spaced 6 mm apart in the poloidal direction.The probe moves inward from250 mm to the center at a speed of10 mm s-1,and each spatial position corresponds to a specific moment in the time series of the probe data.The data for a small period of time0.1 s long near a certain moment is used to calculate thek-spectrumS(kθ,f)for a certain spatial locationr.The calculation method ofS(kθ,f)has been discussed in detail in previous work[16,17].The phase velocity of the mode is calculated as6.3 km s-1,which is close to the ion acoustic velocity calculated byand much slower than the Alfvén speed calculated by

The cross-phase radial distribution of the wave mode with frequency 30 kHz is shown in figure 4.The abscissa is radial position in mm,and the zero point is set at the position of the lowest floating potential,which is also regarded as the position of the separatrix.The ordinate is the average cross phase of wave modes with frequency from 28 to 32 kHz.The cross phase is calculated similarly to previous research[13]between tips No.1 and Nos.5-9 in the 9-tip probe array.The mode with the largest amplitude near 40 kHz was not used for the phase analysis because of interactions with other modes,which will be discussed in detail in section 5.

According to figure 2,the tip No.1 is outside the separatrix when tips Nos.5-9 are in the separatrix region.Therefore,the cross-phase radial profile at tips Nos.5-9 position could be obtained by regarding tip No.1’s crossphase as reference phase.The cross-phase profiles are almost zero out of the separatrix,which has supported us to obtain reference phase of potential perturbation from tip No.1.The phase radial profiles in separatrix region indicate that the IBW mode has‖≈k0.Thus,the wave is considered as propagating vertically to the magnetic field line due tok⊥?k‖.

Overall,the wave is identified as an IBW based on the following criteria.

i.The frequency of the wave mode we observed is close to but higher than the ion cyclotron frequency.

ii.It manifests as a quasi-electrostatic wave.

iii.The 30 kHz and 46 kHz modes can coincide with theoretically calculated IBW curves.The IBW mode on 30 kHz matches well with the equation(2)in[18-20].

iv.The characteristic low-hybrid frequency is～106Hz in our experiment,which is much higher than the perturbation we found.

Besides the experiment case discussed above with 395 G asymptotic magnetic field,the IBW mode also exists in the cases with asymptotic magnetic field from 315 to 552 G.As shown in figures 5(a)and(b),the maximum of IBW amplitude is near the maximum ofErandin separatrix region,which may provide energy to the IBW mode.Therefore,the separatrix region is suspected to be the origin of IBW.As shown in the auto-spectrums figures 3 and 5(c),there is a significant decrease in the amplitude of IBW fluctuations atr=100 mm andr=107 mm near the separatrix region,where the cross-phase angle in figure 3(c)also changes abruptly.The wave damping induced by ion-neutral collision could be estimated throughwhereIm(k⊥),viiandvg⊥denote IBW collisional damping rate,ion-neutral collision frequency and the IBW group velocity vertical to the magnetic field line.Ion-neutral collision frequency is7.7 ×104s-1based on the result of previous work.vg～vp≈6.3 km s-1because the phase velocities for different IBW modes have no significant change in figure 3.

The IBW modes we observed in the separatrix region are quasi-electrostatic wave modes with frequenciesω≤2ωci?ωLH,wave vectorand phase velocitiesvp～Cs.Figure 3(c)clearly shows that the phase difference between IBW’sandchanges repeatedly near the separatrix,which means that the modes may drive particle flux across the separatrix.Related contents will be further discussed in the next section.

Figure 4.The cross-phase radial profile of with frequencies from 28 to 32 kHz.Tip No.1 is regarded as the reference probe.The region presented by profiles is marked in the figure 2.

Figure 5.Ion density profile,floating potential profile,amplitude of IBW,and plasma flow in separatrix region.(a)Ion density profile in m -3 and (b)Floating potential profile in V and Er profile in V m-1.(c)Normalized IBW perturbations.Amplitude ofis normalized byand amplitude ofis normalized byVertical particle flux driven by IBW(red line),low-frequency wave modes(cyan line)and plasma flux parallel to the magnetic field line measured by Mach probe(blue line).Γin the ordinate is the flux normalized by n 0 Cs,where n0 is local plasma ion density andCs is ion acoustic speed.S is the cross-sectional area through which the fluxes flow.

Figure 6.Diagram of the flux in separatrix area.

Figure 7.self-bio-coherence in different positions:(a)50-51 mm,(b)104-105 mm.

4.Particle transport driven by the IBWs

The particle flux can be calculated by bringing the above physical quantities into equation(5),in which the angle bracket indicates the time average of signals over0.025 s.Considering that our probe’s velocity is 10 mm s-1,the spatial resolution of particle flux calculations is 0.25 mm.

The measured parallel plasma flow and the radial particle flux generated by perturbations near the separatrix region is illustrated in figure 5(d).The red line represents the flux driven by IBW perturbations from 26 to 50 kHz,and the flux driven by low-frequency wave modes from 0.5 to 15 kHz is shown by green line and two orders of magnitudes smaller than that driven by IBW.The particle transport caused by IBW is more than an order of magnitude larger than the particle transport caused by perturbations at lower frequencies and on the same order of magnitude as the plasma flow in the parallel direction.Therefore,we can assume that IBW induces significant transport near the separatrix region.

Figure 6 is a diagram based on figure 5(d)for the fluxes in the magnetic-null configuration.The shaded region illustrates the separatrix region.The yellow line is the parallel plasma flow that is measured by Mach probes and assumed to flow through a torus section.The blue line indicates the radial ion flux that is driven by IBW and assumed to flow through a spherical surface.The total particle transport in the separatrix region can be obtained by the particle flux density timesΓthe area crossed by the particle flowS,which can be calculated by equation(6)for transport perpendicular to the magnetic field line and by equation(7)for transport parallel to the magnetic field line.

Figure 8.Bi-coherence between

5.Conclusion and discussion

There are several possible mechanisms for IBW generation suggested in previous research,such as mode conversion from Alfvén wave to IBW which were studied in space plasma theory[20]and tokamak heating experiment[21],as well as by the ion Bernstein instability due toat suprathermal perpendicular speeds[22].

As shown in figures 5(a)and(b),parallel magnetic plasma flux with approximately 0.2 Mach number in separatrix region and theErandin separatrix region could drive poloidalfrom=r 104 to=r 105 mm.folw.ConsideringTi～0.3 eVin this case,the velocity of the parallel plasma flow and the velocity of the flow generated by the electric field gradient and the density gradient are greater than the velocity of the thermal motion of the ions.Therefore,we suppose the formation mechanisms of IBW in this case may be due towhich resembles predecessors’research [20].The further research will be scheduled to clarify this topic in the future.

In this work,it is identified that the IBW exists in the separatrix near the null.The IBW modes have multi-frequency components.This may be due to the wave-wave interaction between IBW and other mode.Figures 3(a)and(b),the autospectra of the plasma density and the floating potentials,show that there is a low frequency perturbation mode at about 8 kHz,which is found to have interaction with IBW in figure 8.By comparingself-bio-coherence in different positions,we find that the nonlinear interaction is stronger in the separatrix region.Figure 7 indicates the bi-coherence betweenandon separatrix,which also suggests the wave-wave interaction between the IBW and the low frequency mode.The frequencies of low frequency mode and IBW follow equation(8).The interaction probably causes the equal frequency interval between IBW components

fIBWiindicates the different components of IBW modes.

Considering the previous studies[12,23],the low frequency mode might be some drift waves.Further study is needed to the suspected drift waves and the wave-wave interactions on separatrix.

As mentioned above,due to the asynchronism betweenandthe IBW mode could drive particle fulxes,i.e.increasing the particle diffusion across magnetic lines,in the separatrix region.The transport levels from the radial particle flux driven by IBW and the parallel flow measured by Mach probe are on the same magnitude.Therefore,this effect could not only increase the particle exchange near the boundary of open field line region and closed field line region,but also have an important role during the formation of equilibrium profiles,which may cause an inhomogeneous distribution of electrons and ions and thus acceleration of ions and electrons through electric fields in the separatrix region.For the importance of IBW’s transport effect in the separatrix region,further studies should focus on the IBW properties in the separatrix region.

The mechanism of the IBW generation,and its role during the reconnection process need further studies.We will investigate the interaction between IBW and the low frequency modes,as well as IBW during 3D reconnection in the near future.

Acknowledgments

This work was supported by National Natural Science Foundation of China(No.11975038)and the National MCF Energy R&D Program of China(Nos.2017YFE0300601 and 2018YFE0311400).