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Study of backward propagating Langmuir waves with PIC simulation
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Advances in Space Research 41 (2008) 1202–1205 www.elsevier.com/locate/asr
Study of backward propagating Langmuir waves with PIC simulation
q
Huang Yu *, Huang Guangli Purple Mountain Observatory, 2#, West Beijing Road, Nanjing 210008, China Received 17 October 2006; received in revised form 11 March 2007; accepted 24 June 2007
Abstract The conversion of Langmuir waves into electromagnetic radiations is an important mechanism of solar type III bursts. Langmuir waves can be easily excited by electron beam instability, and they can be converted into backward propagating Langmuir waves by wave–wave interaction. Generally, the backward propagating Langmuir waves are very important for the second harmonic emission of solar type III bursts. In this work, we pay particular attention to the mechanism of the backward propagating Langmuir waves by particle in cell (PIC) simulations. It is confirmed that the ions play a key role in exiting the backward propagating Langmuir waves. Moreover, the electron beam can hardly generated the backward propagating Langmuir waves directly, but may directly amplify the second harmonic Langmuir waves. Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Type III bursts; Backward propagating Langmuir wave
1. Introduction Langmuir waves (LW) are one of the most typical and significant plasma waves observed in solar and space plasma, and LW can be easily excited by electron beam instability, when the fast electrons accelerated in low corona travel outward along magnetic field lines through high corona and interplanetary space. The interaction between the ambient plasma and fast electrons generates the intensive LW at the local plasma frequency. After that, a part of the energy of LW may be converted into the electromagnetic radiations either at the fundamental, f = fp, or the second harmonic, f = 2fp, or both (Ginzburg and Zheleznyakov, 1958), and defined as type III bursts. When the fast electrons travel through corona and interplanetary space, the density of the ambient plasma will be continuously reduced, as well as the local plasma frequency, to explain the rapid frequency drifts of type III bursts. It is
q This study is supported by the NFSC projects No. 10333030, and ‘‘973’’ program with No. 2006CB806302. * Corresponding author. E-mail address: [email protected] (H. Yu).
generally accepted that the fundamental plasma emissions are caused by scattering of LW into transverse waves with plasma particles, and the second harmonic emissions are produced through coalescence of two LW, i.e., the forward propagating LW and the backward propagating LW, which generated through the forward propagating LW scattered by ions sound waves, to form transverse waves at the second harmonic (Melrose, 1991). With above-mentioned theory as background, some computer experiments have been done to understand the process of the type III bursts generated. The particle-in-cell (PIC) simulations were performed used 1-D and 2-D electromagnetic code, called Kyoto ElectroMagnetic Particle cOdes (KEMPO) by Kasaba et al. (2001). In both of 1-D and 2-D systems, the forward and the backward propagating LW at the plasma frequency f = fp and the second harmonic f = 2fp can be excited. The electromagnetic waves are produced at both of the fundamental and the second harmonic in the 2-D system. The time evolutions of the intensity of different plasma waves show that there is no correlation between the forward and the backward propagating LW. The electrostatic LW at 2fp are correlated with the beam-excited LW, while the electromagnetic waves at 2fp are correlated with the backward propagating LW.
0273-1177/$34 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.06.058
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
2. Simulations The simulations are performed by using an 1-D electrostatic code (KEMPO) with periodic condition, and the direction of magnetic field along the direction of beam electrons. Firstly, we assume two groups of electrons, beam and background electrons, but without ions in the simulations. The simulations without ions means the ions are fixed. They cannot be moved by electromagnetic field, but the charge neutrality is still kept. Then we get a panel of dispersion relation Fig. 1, in which the forward and backward propagating LW at the fundamental, f = fp, and the forward propagating LW at the second harmonic, f = 2fp, can be seen. Then, the simulation is performed with the beam electrons, ambient electrons and ions, and we can also get the spectra, which are almost same as Fig. 1. In order to compare the difference of the simulations with and without ions, we cut out three rectangles, the forward propagating LW in S1, the backward propagating LW in S2, and the second harmonic LW in S3. The time evolutions of the intensity of different plasma waves are obtained by reverse Fourier transforming in each area of S1, S2, S3,
2.4
2
←S
3
ω/ωpe
The PIC simulations of solar type III bursts were also studied recently by Li et al. (2006a,b). They considered beam and wave dynamics, included the effects of regular density gradient and irregular density fluctuations, and presented the large-scale evolution of the type III system. For bidirectional coronal emissions, they found that both fundamental and harmonic emission in the upward direction are stronger than downward, consistent with observations and theory. They also studied the statistics of Langmuir fields. They found that Langmuir and ion sound waves are bursty, and the statistics of LW energy agree well with the predictions of stochastic growth theory, the electrostatic decay process is slaved to the evolution of the primary beam-Langmuir waves. So PIC simulation is a new tendency to study the details of solar type III bursts. Recently, we have already studied the dispersion relation of backward propagation LW by analytical and PIC simulations (Yu and Guangli, accepted by AcAsn). In the analytical work, we found that the dispersion relation of LW of k < 0 varies with the electron temperature, and the phase velocity increases with the electron temperature. The LW of k > 0 propagate due to the beam electrons, so the phase velocity increases obviously with the speed of beam electrons, but it is less sensitive to the electron temperature. In the PIC simulations, we found only a part of comparable results with the analytical work. However, the details of the generation mechanism of the backward propagating LW are still unclear. To understand the generation mechanism of backward propagating LW, we perform computer experiments with two different conditions, one is beam–ambient plasma interaction, and the other one is wave–ambient plasma interaction. In each condition, we performed the simulations with the ambient ions and without ions, respectively.
1203
1.6
1
S2 →
-2
← S1
-1
0 K
1
2
Fig. 1. The spectra obtained by Fourier transforming of logarithm electric field in space along X axis.
as shown in Fig. 2. In panels (a) and (b) of Fig. 2, the LW at the fundamental and the second harmonic both have fast growth at first, then they got to saturate at almost the same time. The backward propagating LW almost have zero growth rate in panel (a), but have obviously grew in panel (b) which is simulated with ions. In our simulations, the maximum powers of the backward propagating LW are 1.25 percent and 7.40 percent of that of the forward propagating LW in panel (a) and (b) of Fig. 2, respectively. So, the ions are very important to the growth rate of backward propagating LW. On the other hand, the maximum powers of the second harmonic LW are 0.40 percent and 0.31 percent of that of the forward propagating LW. Secondly, we use the forward propagating LW instead the beam electrons, as the free energy to excite the backward propagating LW and the forward propagating LW at the second harmonic. In this way, we want to check qualitatively if the backward propagating LW and second harmonic LW are excited by beam electrons or by the forward propagating LW. The simulations were performed only with the ambient electrons, at the first few steps, we add the electric field of the forward propagating LW, according to that of Fig. 2. So, the ambient electrons moved both in the self-generated electric field and extent LW electric field. After the energy of electric field got to the level of the total energy of the plasma waves, we take away the extra waves which excited by electron beam, and see how did the plasma waves evolve. Some time later, the energy of forward propagating LW was converted to backward propagating LW, then we control the total energy of the plasma waves as same as in Fig. 2. Then we got the spectra. After that, we add the ambient ions in the simulations. We can also get the panel of dispersion relation that similar to Fig. 1. Still we calculated the time evolutions of the power density of different plasma waves with and without ions, as shown in Fig. 3. Both panels show that there are obviously correlation between the LW at the fundamental and the second har-
1204
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
without ions
with ions
10-7
10-7 L
L
10-8
10-9
L’
10-10
ES-2fp
10-11
50
100
150 200 ω-1 p
wave energy
wave energy
10-8
250
300
10-9
L’
10-10
ES-2fp
10-11
50
100
150 200 ω-1 p
250
300
Fig. 2. Evolutions of the power density of different plasma waves in (a) without ions and (b) with ions, when the electron beam exists. Plotted data are power density of forward propagating LW (L), backward propagating LW (L 0 ) and electrostatic 2fp wave (ES 2fp).
without ions
with ions
10-7
10-7
L
L 10-8
10-9
L’
10-10
10-11
wave energy
wave energy
10-8
10-10
ES-2fp
50
100
150
200
L’
10-9
250
300
ω-1 p
10-11
ES-2fp
50
100
150
200
250
300
ω-1 p
Fig. 3. Evolutions of the power density of different plasma waves in (a) without ions and (b) with ions, when the electron beam is replaced by the LW which generated by the beam instability. Plotted data are power density of forward propagating LW (L), backward propagating LW (L 0 ) and electrostatic 2fp wave (ES 2fp).
monic, which is almost same as Fig. 2. In these simulations, the maximum powers of backward propagating LW are 1.56 percent and 8.08 percent of that of the forward propagating LW in panel (a) and (b) of Fig. 3, respectively. The power ratios of backward and forward propagating LW in Fig. 3 are similar to that of in Fig. 2. On the other hand, the maximum powers of the second harmonic LW are 0.15 percent and 0.16 percent of that of the forward propagating LW. So, the ratios are evidently smaller than that of in Fig. 2. 3. Discussions At first, we simulated the beam electron instability, and we got that the ions are very important in the growth rate of the backward propagating LW. When the simulation is performed without ions, the generation mechanism of backward propagating LW is only due to the thermal disturbance, so, it has a very small growth rate. But, in the simulations with ions, the backward propagating LW gen-
erated through the forward propagating LW scattered by ions sound waves. It is a continue process, so the backward propagating LW have a long time growing. By the way, when the ions temperature increasing, the growth rate increased obviously. Then we got rid of the beam electrons, and used the forward propagating LW which generated by beam electrons instead. The backward propagating LW also have a great growth rate in the simulation with ions. Through both Figs. 2 and 3 we can say that the backward propagating LW depended on the ions and the forward propagating LW, and in these simulations with or without electron beam, we got the almost same power density and time evolution of backward propagating LW. So, we can say that the electron beam can hardly generated the backward propagating LW directly. Moreover, in all simulations, the fundamental and the second harmonic LW has a obviously correlation. They grew and got to saturation almost at the same time. But, we should notice that the power density of the second har-
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
monic LW in Fig. 2 is about two times larger than that of in Fig. 3, hence, the electron beam may amplify the second harmonic LW directly. By now, we confirm that the ions play an important role in the generation mechanism of the backward propagating LW, and we also know that the electron beam can hardly generated the backward propagating LW directly. Therefore, we almost know the property of the electrostatic waves associated with type III bursts. Next, we are going to work on the property of the electromagnetic waves in type III bursts by using 2-D electromagnetic PIC simulations.
1205
References Ginzburg, V.L., Zheleznyakov, V.V. Soviet Astronomy Letters 2, 653– 667, 1958. Kasaba, Y., Matsumoto, H., Omura, Y. JGR 106 (A9), 18693–18712, 2001. Li, Bo, Robinson, Peter A., Cairns, Iver H. Physical Review Letters 96, 145005, 2006a. Li, Bo, Robinson, Peter A., Cairns, Iver H. Physics Of Plasmas 13, 092902, 2006b. Melrose, D.B. Annual Review of Astronomy and Astrophysics 29, 31–57, 1991. Huang Yu and Huang Guangli. Acta Astronomical Sinica. accepted for publication.
Advances in Space Research 41 (2008) 1202–1205 www.elsevier.com/locate/asr
Study of backward propagating Langmuir waves with PIC simulation
q
Huang Yu *, Huang Guangli Purple Mountain Observatory, 2#, West Beijing Road, Nanjing 210008, China Received 17 October 2006; received in revised form 11 March 2007; accepted 24 June 2007
Abstract The conversion of Langmuir waves into electromagnetic radiations is an important mechanism of solar type III bursts. Langmuir waves can be easily excited by electron beam instability, and they can be converted into backward propagating Langmuir waves by wave–wave interaction. Generally, the backward propagating Langmuir waves are very important for the second harmonic emission of solar type III bursts. In this work, we pay particular attention to the mechanism of the backward propagating Langmuir waves by particle in cell (PIC) simulations. It is confirmed that the ions play a key role in exiting the backward propagating Langmuir waves. Moreover, the electron beam can hardly generated the backward propagating Langmuir waves directly, but may directly amplify the second harmonic Langmuir waves. Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Type III bursts; Backward propagating Langmuir wave
1. Introduction Langmuir waves (LW) are one of the most typical and significant plasma waves observed in solar and space plasma, and LW can be easily excited by electron beam instability, when the fast electrons accelerated in low corona travel outward along magnetic field lines through high corona and interplanetary space. The interaction between the ambient plasma and fast electrons generates the intensive LW at the local plasma frequency. After that, a part of the energy of LW may be converted into the electromagnetic radiations either at the fundamental, f = fp, or the second harmonic, f = 2fp, or both (Ginzburg and Zheleznyakov, 1958), and defined as type III bursts. When the fast electrons travel through corona and interplanetary space, the density of the ambient plasma will be continuously reduced, as well as the local plasma frequency, to explain the rapid frequency drifts of type III bursts. It is
q This study is supported by the NFSC projects No. 10333030, and ‘‘973’’ program with No. 2006CB806302. * Corresponding author. E-mail address: [email protected] (H. Yu).
generally accepted that the fundamental plasma emissions are caused by scattering of LW into transverse waves with plasma particles, and the second harmonic emissions are produced through coalescence of two LW, i.e., the forward propagating LW and the backward propagating LW, which generated through the forward propagating LW scattered by ions sound waves, to form transverse waves at the second harmonic (Melrose, 1991). With above-mentioned theory as background, some computer experiments have been done to understand the process of the type III bursts generated. The particle-in-cell (PIC) simulations were performed used 1-D and 2-D electromagnetic code, called Kyoto ElectroMagnetic Particle cOdes (KEMPO) by Kasaba et al. (2001). In both of 1-D and 2-D systems, the forward and the backward propagating LW at the plasma frequency f = fp and the second harmonic f = 2fp can be excited. The electromagnetic waves are produced at both of the fundamental and the second harmonic in the 2-D system. The time evolutions of the intensity of different plasma waves show that there is no correlation between the forward and the backward propagating LW. The electrostatic LW at 2fp are correlated with the beam-excited LW, while the electromagnetic waves at 2fp are correlated with the backward propagating LW.
0273-1177/$34 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.06.058
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
2. Simulations The simulations are performed by using an 1-D electrostatic code (KEMPO) with periodic condition, and the direction of magnetic field along the direction of beam electrons. Firstly, we assume two groups of electrons, beam and background electrons, but without ions in the simulations. The simulations without ions means the ions are fixed. They cannot be moved by electromagnetic field, but the charge neutrality is still kept. Then we get a panel of dispersion relation Fig. 1, in which the forward and backward propagating LW at the fundamental, f = fp, and the forward propagating LW at the second harmonic, f = 2fp, can be seen. Then, the simulation is performed with the beam electrons, ambient electrons and ions, and we can also get the spectra, which are almost same as Fig. 1. In order to compare the difference of the simulations with and without ions, we cut out three rectangles, the forward propagating LW in S1, the backward propagating LW in S2, and the second harmonic LW in S3. The time evolutions of the intensity of different plasma waves are obtained by reverse Fourier transforming in each area of S1, S2, S3,
2.4
2
←S
3
ω/ωpe
The PIC simulations of solar type III bursts were also studied recently by Li et al. (2006a,b). They considered beam and wave dynamics, included the effects of regular density gradient and irregular density fluctuations, and presented the large-scale evolution of the type III system. For bidirectional coronal emissions, they found that both fundamental and harmonic emission in the upward direction are stronger than downward, consistent with observations and theory. They also studied the statistics of Langmuir fields. They found that Langmuir and ion sound waves are bursty, and the statistics of LW energy agree well with the predictions of stochastic growth theory, the electrostatic decay process is slaved to the evolution of the primary beam-Langmuir waves. So PIC simulation is a new tendency to study the details of solar type III bursts. Recently, we have already studied the dispersion relation of backward propagation LW by analytical and PIC simulations (Yu and Guangli, accepted by AcAsn). In the analytical work, we found that the dispersion relation of LW of k < 0 varies with the electron temperature, and the phase velocity increases with the electron temperature. The LW of k > 0 propagate due to the beam electrons, so the phase velocity increases obviously with the speed of beam electrons, but it is less sensitive to the electron temperature. In the PIC simulations, we found only a part of comparable results with the analytical work. However, the details of the generation mechanism of the backward propagating LW are still unclear. To understand the generation mechanism of backward propagating LW, we perform computer experiments with two different conditions, one is beam–ambient plasma interaction, and the other one is wave–ambient plasma interaction. In each condition, we performed the simulations with the ambient ions and without ions, respectively.
1203
1.6
1
S2 →
-2
← S1
-1
0 K
1
2
Fig. 1. The spectra obtained by Fourier transforming of logarithm electric field in space along X axis.
as shown in Fig. 2. In panels (a) and (b) of Fig. 2, the LW at the fundamental and the second harmonic both have fast growth at first, then they got to saturate at almost the same time. The backward propagating LW almost have zero growth rate in panel (a), but have obviously grew in panel (b) which is simulated with ions. In our simulations, the maximum powers of the backward propagating LW are 1.25 percent and 7.40 percent of that of the forward propagating LW in panel (a) and (b) of Fig. 2, respectively. So, the ions are very important to the growth rate of backward propagating LW. On the other hand, the maximum powers of the second harmonic LW are 0.40 percent and 0.31 percent of that of the forward propagating LW. Secondly, we use the forward propagating LW instead the beam electrons, as the free energy to excite the backward propagating LW and the forward propagating LW at the second harmonic. In this way, we want to check qualitatively if the backward propagating LW and second harmonic LW are excited by beam electrons or by the forward propagating LW. The simulations were performed only with the ambient electrons, at the first few steps, we add the electric field of the forward propagating LW, according to that of Fig. 2. So, the ambient electrons moved both in the self-generated electric field and extent LW electric field. After the energy of electric field got to the level of the total energy of the plasma waves, we take away the extra waves which excited by electron beam, and see how did the plasma waves evolve. Some time later, the energy of forward propagating LW was converted to backward propagating LW, then we control the total energy of the plasma waves as same as in Fig. 2. Then we got the spectra. After that, we add the ambient ions in the simulations. We can also get the panel of dispersion relation that similar to Fig. 1. Still we calculated the time evolutions of the power density of different plasma waves with and without ions, as shown in Fig. 3. Both panels show that there are obviously correlation between the LW at the fundamental and the second har-
1204
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
without ions
with ions
10-7
10-7 L
L
10-8
10-9
L’
10-10
ES-2fp
10-11
50
100
150 200 ω-1 p
wave energy
wave energy
10-8
250
300
10-9
L’
10-10
ES-2fp
10-11
50
100
150 200 ω-1 p
250
300
Fig. 2. Evolutions of the power density of different plasma waves in (a) without ions and (b) with ions, when the electron beam exists. Plotted data are power density of forward propagating LW (L), backward propagating LW (L 0 ) and electrostatic 2fp wave (ES 2fp).
without ions
with ions
10-7
10-7
L
L 10-8
10-9
L’
10-10
10-11
wave energy
wave energy
10-8
10-10
ES-2fp
50
100
150
200
L’
10-9
250
300
ω-1 p
10-11
ES-2fp
50
100
150
200
250
300
ω-1 p
Fig. 3. Evolutions of the power density of different plasma waves in (a) without ions and (b) with ions, when the electron beam is replaced by the LW which generated by the beam instability. Plotted data are power density of forward propagating LW (L), backward propagating LW (L 0 ) and electrostatic 2fp wave (ES 2fp).
monic, which is almost same as Fig. 2. In these simulations, the maximum powers of backward propagating LW are 1.56 percent and 8.08 percent of that of the forward propagating LW in panel (a) and (b) of Fig. 3, respectively. The power ratios of backward and forward propagating LW in Fig. 3 are similar to that of in Fig. 2. On the other hand, the maximum powers of the second harmonic LW are 0.15 percent and 0.16 percent of that of the forward propagating LW. So, the ratios are evidently smaller than that of in Fig. 2. 3. Discussions At first, we simulated the beam electron instability, and we got that the ions are very important in the growth rate of the backward propagating LW. When the simulation is performed without ions, the generation mechanism of backward propagating LW is only due to the thermal disturbance, so, it has a very small growth rate. But, in the simulations with ions, the backward propagating LW gen-
erated through the forward propagating LW scattered by ions sound waves. It is a continue process, so the backward propagating LW have a long time growing. By the way, when the ions temperature increasing, the growth rate increased obviously. Then we got rid of the beam electrons, and used the forward propagating LW which generated by beam electrons instead. The backward propagating LW also have a great growth rate in the simulation with ions. Through both Figs. 2 and 3 we can say that the backward propagating LW depended on the ions and the forward propagating LW, and in these simulations with or without electron beam, we got the almost same power density and time evolution of backward propagating LW. So, we can say that the electron beam can hardly generated the backward propagating LW directly. Moreover, in all simulations, the fundamental and the second harmonic LW has a obviously correlation. They grew and got to saturation almost at the same time. But, we should notice that the power density of the second har-
H. Yu, H. Guangli / Advances in Space Research 41 (2008) 1202–1205
monic LW in Fig. 2 is about two times larger than that of in Fig. 3, hence, the electron beam may amplify the second harmonic LW directly. By now, we confirm that the ions play an important role in the generation mechanism of the backward propagating LW, and we also know that the electron beam can hardly generated the backward propagating LW directly. Therefore, we almost know the property of the electrostatic waves associated with type III bursts. Next, we are going to work on the property of the electromagnetic waves in type III bursts by using 2-D electromagnetic PIC simulations.
1205
References Ginzburg, V.L., Zheleznyakov, V.V. Soviet Astronomy Letters 2, 653– 667, 1958. Kasaba, Y., Matsumoto, H., Omura, Y. JGR 106 (A9), 18693–18712, 2001. Li, Bo, Robinson, Peter A., Cairns, Iver H. Physical Review Letters 96, 145005, 2006a. Li, Bo, Robinson, Peter A., Cairns, Iver H. Physics Of Plasmas 13, 092902, 2006b. Melrose, D.B. Annual Review of Astronomy and Astrophysics 29, 31–57, 1991. Huang Yu and Huang Guangli. Acta Astronomical Sinica. accepted for publication.