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Polar mesosphere summer echoes (PMSEs) are strong radar echoes produced at polar latitude during the summer. This phenomenon is the first time observed with 50 MHz MST radar at Poker Flat, Alaska[1]. The occurrence altitude of PMSE is about 80~90 km, and the strongest echo is usually observed at about 85 km. Since its first observation at 50 MHz, PMSE have been observed at a variety of frequencies between 2.78 and 1290 MHz. Many scientists of space and dusty plasma physics diverted their attentions to these interesting radar phenomena and achieved a lot of diagnostic information[2].
It is now well understood that charged ice particles play a crucial role in the charge balance of the polar summer mesosphere region where ice particles become negatively charged due to electron attachment and hence effectively scavenge electrons[3-9]. This process results in electron density depletions or the so-called electron ‘bite-outs’[10]. Fluctuations in electron density are generally anti-correlated to the negative dust charge density, however, in certain regions, it is also positively correlated[11]. Recently, in the Earth ionosphere the effect of charged dust particles on radar observations was discussed[12]. Also, a new method for the analysis of the measurements of mesospheric dust was presented[13]. The occurrence of ‘bite-outs’ is hence considered as strong support for the existence of mesospheric ice particles. So far, electron ‘bite-outs’ in the vicinity of PMSE have routinely been observed with the rocket-borne sensors[10,14-16]as well as occasionally with ground-based radars[17-18].
Study of dusty plasma is important for a number of applications in laboratory plasmas and modern plasma technologies, as well as in space plasmas and plasma of the Earth’s environment[19-20]. Scattering of electromagnetic waves in plasma is a powerful diagnostic method that has been successfully used in the laboratory and ongoing geophysical experiments[21-25].
Rocket experiments have been used to detect PMSE. In the rocket experiments, there is equipped with a dust probe (DUSTY) for measuring dust current and an electron probe (CONE) for measuring neutral atmospheric parameters and electron currents. When the rocket moves through the mesopause, the charged dust particles and electrons collide with the DUSTY and CONE probe respectively and generate current. Then the dust current and electron current were recorded. In addition, the temperature of the mesosphere can be measured[13,26-27]. However, in these experiments the radius and charge of dust particles are not measured accurately. But it is suggested that the dust charge number can be obtained by the charging process of electron and ion to dust particles. Later, PMSE heating experiments also detect the dust particles in the polar mesosphere, however, we still lack numerical simulation about the charged dust particles causing PMSE[28-29]. So, it is necessary to analyze the size of dust particles and estimate the electric charge by theory and simulation.
In this paper, using the orbit-limited motion (OLM) method and the charging theory of dust particles, the formula for dust charge is deduced in dusty plasma. The experimental data of ECT-02 is used to analyze the charge number of dust particle in the PMSE dusty plasma region (80~90 km).
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In the mesosphere, since photoelectron emission is negligible, the charging process of electron and ion to dust particles is only due to the collection of plasma particles where the charge number on each dust particles will be low (typically a few unit charges or less) and negative. The OLM theory is one of the most popular sphere-charging model[30]. The OLM method is based on the electron/ion Maxwell distribution to decide the electron/ion current carried on dust particles[31-33]. The OLM method and the charging theory of dust particles in dusty plasma are used to obtain the relation of dust particles radius and dust charge number with different electron temperatures. When the active experiments of PMSE are carried out, the electron temperature will change greatly, and many other parameters in PMSE dusty plasma layer will have corresponding changes at different time scales. To the best of our knowledge, the charging effects of dust particles in polar has not been yet addressed within the experimental framework[34-36].
By using the OLM method, the charging current to the dust grain carried out by the plasma particles are given as:
$${I_{\rm{e}}} = - {\rm{ }}\sqrt {{\rm{8{\text π} }}} r_{\rm{d}}^2{n_{\rm{e}}}{\rm{e}}{\upsilon _{{\rm{te}}}}{\rm{exp}}\left( {{{ - {\rm{e}}{\phi _{\rm{d}}}} / {{k_{\rm{B}}}{T_{{e}}}}}} \right)$$ (1) $${I_{\rm{i}}} = {\rm{ }}\sqrt {8{{\text π}}} r_{\rm{d}}^2{n_{\rm{i}}}{\rm{e}}{\upsilon _{{\rm{ti}}}}\left( {1 - {{{\rm{e}}{\phi _{\rm{d}}}} / {{k_{\rm{B}}}{T_{\rm{i}}}}}} \right)$$ (2) where Ie and Ii represent the charging currents of electron and ion, respectively;
${k_{\rm{B}}} = 1.38 \times {10^{ - 23}}{\rm{J}} \cdot {{\rm{K}}^{ - 1}}$ is Boltzmann constant;${r_{\rm{d}}}$ and${\phi _{\rm{d}}}$ are the dust radius and floating potential; ne, me, and Te are the electron density, mass and temperature, respectively; ni, mi, and Ti are ion density, mass and temperature, respectively;${\upsilon _{{\rm{te}}}} = {\left( {{{{k_{\rm{B}}}{T_{\rm{e}}}} / {{m_{\rm{e}}}}}} \right)^{{1 / 2}}}$ and${\upsilon _{{\rm{ti}}}} = {\left( {{{{k_{\rm{B}}}{T_{\rm{i}}}} / {{m_{\rm{i}}}}}} \right)^{{1 / 2}}}$ are the electron and ion thermal velocities, respectively.The dust grain surface becomes negatively charged and Ii<<Ie (since me<<mi) when the number density of electron and ion have great differences. However, in the case of electron ‘bite-outs’ condition when the ion density is much larger than electron density, the ion and electron currents have no difference given as:
$${I_{\rm{e}}} + {I_{\rm{i}}} = 0$$ (3) When no external disturbance is present, like electron-ion plasma, the dusty plasma is also macroscopically neutral. It means that in equilibrium with no external forces present, the net resulting electric charge in dusty plasma is zero. Therefore, the equilibrium charge neutrality condition in dusty plasma can be written as:
$${q_{\rm{i}}}{n_{\rm{i}}} - {\rm{e}}{n_{\rm{e}}} - {q_{\rm{d}}}{n_{\rm{d}}} = 0$$ (4) where ns is the unperturbed number density of the plasma species s (where s = ion or electron and d=dust);
${q_{\rm{i}}}$ and${q_{\rm{d}}}$ are the charges of ion and dust, respectively. It is already confirmed that the dust particles in the mesosphere are mostly negatively charged.We assume that
${Z_{\rm{d}}} = - {{4{\text π} {\varepsilon _0}{r_{\rm{d}}}{\phi _{\rm{d}}}} / {\rm{e}}}$ is the number of charges residing on the dust grain surface. Here,${\varepsilon _0}$ is the permittivity of vacuum. At the same time, we assume that the ion charge state Zi=1 will be used in the rest of the paper. So equation (4) changes into:$${n_{\rm{i}}} = {n_{\rm{e}}} + \left| {{Z_{\rm{d}}}} \right|{n_{\rm{d}}}$$ (5) By combining the obtained equations (1), (2), (3) and (5), it can be obtained:
$${\left( {\frac{{{T_{\rm{i}}}{m_{\rm{e}}}}}{{{T_{\rm{e}}}{m_{\rm{i}}}}}} \right)^{{1 / 2}}}\left( {1 - \frac{{{\rm{e}}{\phi _{\rm{d}}}}}{{{k_{\rm{B}}}{T_{\rm{i}}}}}} \right)\exp \left( { - \frac{{{\rm{e}}{\phi _{\rm{d}}}}}{{{k_{\rm{B}}}{T_{\rm{e}}}}}} \right) = 1 - \frac{{{Z_{\rm{d}}}{n_{\rm{d}}}}}{{{n_{\rm{i}}}}}$$ (6) In the paper the unit of rd is nm; Te and Ti are the temperatures of electron and ion, with unit K, respectively. The mass of an electron is me=9.1×10−31 kg and the mass of an ion is mi=4.98×10−26 kg (where the main components are O2+ and NO+, respectively). The charge of an electron is e=1.6×10−19 C;
${Z_{\rm{d}}}{n_{\rm{d}}}$ is the dust charge number density.Finally, the dust charge number is determined by the size of the dust radius, electron temperature, ion temperature, ion number density, and electron number density.
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摘要: 利用轨道运动限制和尘埃带电理论,分析了在极区中层顶中,尘埃等离子体受高功率无线电磁波的影响下,尘埃粒子的带电效应。此外,利用数值模拟及实验方法对理论分析结果进行了验证。通过理论分析可知,尘埃粒子带电数由尘埃半径大小、电子温度、离子温度的高低以及离子数密度和电子数密度决定。通过数值模拟及统计分析火箭探测数据得到,平均尘埃带电数随等离子体中尘埃电荷数密度的增加而降低,而随尘埃半径、电子温度和电子密度的增加而增加。在一定程度上,仿真及实验结果与理论研究结果较一致,当尘埃带电量为0.4e时,尘埃半径值与文献结果一致。Abstract: By using the orbit-limited motion (OLM) method and the charging theory of dust particles, the charging effects of dust particles during the condition when dusty plasmas in mesosphere affected by high power radio wave are analyzed in this paper. In addition, the theoretical results are demonstrated by simulated experiments. Through theoretical analysis, it can be known that the number ofcharge dust particles is determined by the size of the dust radius, electron temperature, ion temperature, ion density and electron density. Based on the data of rocket-borne sensors and simulation results, it is found that the average number of charged dust decreases with an increase in dust charges number density and increases with an increase in dust radius, electron temperature, and electron density. The simulation results are close to the theoretical and experimental studied results, and the average radius are consistent with the results of reference when the average dust charge is 0.4e.
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Key words:
- dust charge number /
- dust particles /
- dusty plasma /
- orbit-limited motion
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Figure 2. As Fig. 1, but for electron temperature
Figure 3. As Fig. 1, but for electron number density
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