Fig 4 - uploaded by Herbert Gunell
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The electric field in a z − t diagram. The ion acoustic speed is indicated by the slope of the black line.
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An auroral flux tube is modelled from the mag-netospheric equator to the ionosphere using Vlasov simu-lations. Starting from an initial state, the evolution of the plasma on the flux tube is followed in time. It is found that when applying a voltage between the ends of the flux tube, about two thirds of the potential drop is concentrated in a thin...
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Citations
... In recent years, Vlasov simulations have been used in magnetospheric physics to study, for example, electrostatic acceleration of auroral electrons in the upward (Gunell et al., 2013) and downward (Gunell et al., 2015) current regions, and large-scale simulations of the magnetosphere have been performed of both the nightside (Palmroth et al., 2017) and dayside (Palmroth et al., 2018) regions. Those large-scale simulations employed a hybrid scheme where only the ions were modelled kinetically; the electrons are there as a mere neutralizing fluid. ...
The use of equations and mathematical modelling in magnetospheric and space physics is reviewed. First, the basic equations are discussed. Then, kinetic and fluid theory are treated. The role of approximations and the applicability of the theories in practice are emphasized.
... Vlasov simulations provide additional insight compared to PIC. It is shown that the electron acceleration is practically achieved in the double layer itself, when a total potential drop, , is assumed (Gunell et al. 2013). Nevertheless, a third of the final acceleration energy is gained above the DL; also, the DL altitude decreases with increasing . ...
The theory of the acceleration of auroral particles is reviewed, focusing on developments in the last 15 years. We discuss elementary plasma physics processes leading to acceleration of electrons to energies compatible with emission observed for quiet, discrete auroral arcs, defined as arcs that have time scales of minutes or more and spatial scales ranging from less than 1 km to tens of kilometers. For context, earlier observations are first described briefly. The theoretical fundamentals of auroral particle acceleration are based on the kinetic theory of plasmas, in particular the development of parallel electric fields. These parallel electric fields can either be distributed along the magnetic field lines, often associated with the mirror geometry of the geomagnetic field, or concentrated into narrow regions of charge separation known as double layers. Observations have indicated that the acceleration process depends on whether the field-aligned currents are directed away from the Earth, toward the Earth, or in mixed regions of currents often associated with the propagation of Alfvén waves. Recent observations from the NASA Fast Auroral SnapshoT (FAST) satellite, the ESA satellite constellation Cluster, and the Japanese Reimei satellite have provided new insights into the auroral acceleration process and have led to further refinements to the theory of auroral particle acceleration.
... Numerical simulations show that the largest fraction (about two thirds) of the accelerating potential is concentrated in a double layer (DL) structure (Gunell et al., 2013). Electrons experience an additional acceleration in the region above the DL where the potential is distributed over larger distances. ...
We discuss a method to estimate the properties of a magnetospheric generator using a quasi‐electrostatic magnetosphere‐ionosphere coupling model and in situ or remote sensing observations of discrete quiet arcs. We first construct an ensemble of Vlasov equilibrium solutions for generator structures formed at magnetospheric plasma interfaces. For each generator solution, we compute the ionospheric electric potential from the current continuity equation. Thus, we estimate the field‐aligned potential drop that allows us to assess several properties of the discrete auroral arc, such as the field‐aligned potential difference, the field‐aligned current density, the flux of precipitating energy, and the height‐integrated Pedersen conductance. A minimization procedure based on comparing the numerical results with observations is defined and applied to find which solution of the current continuity equation and which generator model give auroral arc properties that best fit the observations. The procedure is validated in a case study with observations by DMSP and Cluster and can be generalized to other types of data.
... In order to model the plasma in the return current region we use the Vlasov simulation code published by Gunell et al. (2013a). The model is one-dimensional in configuration space and two-dimensional in velocity space. ...
... This means that the widths of double layers and phase space holes will be overestimated by a factor of √ r , but as long as these widths are much smaller than the typical length scales of the overall changes of the plasma properties the exact values of the widths are not important for the results of the simulation. In order to test this method Gunell et al. (2013a) performed a series of four simulation runs, successively decreasing r from 4.98 × 10 8 down to 4.98 × 10 4 , while observing how the gradients got sharper as this series of runs converged to a solution (see Fig. 3c of that paper). In the simulations reported here, r = 8100 is used; the time step is t = 1.0 × 10 −5 s; the grid is nonuniform with the smallest grid cell size, z = 622 m, at the ionosphere and the largest, z = 1.03 × 10 4 m, at the magnetospheric equator. ...
... For more information about the simulation model, see the paper by Gunell et al. (2013a), which also includes the Fortran code itself. The same code has also been used to study trapping and loss of electrons in the upward current region of Table 1. ...
The plasma on a magnetic field line in the downward current region
of the aurora is simulated using a Vlasov model.
It is found that an electric field parallel to the magnetic
fields is supported by a double layer moving toward higher
altitude.
The double layer accelerates electrons upward, and these electrons
give rise to plasma waves and electron phase-space holes through
beam–plasma interaction.
The double layer is disrupted when reaching altitudes
of 1–2 Earth radii where the Langmuir condition no longer
can be satisfied due to the diminishing density of electrons
coming up from the ionosphere.
During the disruption the potential drop is in part carried
by the electron holes.
The disruption creates favourable conditions for double layer
formation near the ionosphere and double layers form anew
in that region. The process repeats itself with a period of
approximately 1 min.
This period is determined by how far the double layer can reach
before being disrupted: a higher disruption altitude corresponds
to a longer repetition period. The disruption altitude is, in turn,
found to increase with ionospheric density and to decrease
with total voltage.
The current displays oscillations around a mean value. The period
of the oscillations is the same as the recurrence period of the
double layer formations. The oscillation amplitude increases
with increasing voltage, whereas the mean value of the current is
independent of voltage in the 100 to 800 V range covered by our
simulations. Instead, the mean value of the current is determined
by the electron density at the ionospheric boundary.
... Since auroral potential differences are changing with time, we allow the potential to evolve, and particles can be caught and trapped during the formation of a potential profile. Gunell et al. (2013a) found that an electron population became trapped between a double layer and the magnetic mirror field at lower altitudes. It has also been found that fluctuations are an important influence on the electron distributions, leading to electron conics such as those observed by the Viking satellite (André and Eliasson, 1992;Eliasson et al., 1996). ...
... We study the trapped and precipitating electron populations through the use of a Vlasov simulation code that is onedimensional in space and two-dimensional in velocity space (Gunell et al., 2013a). This model was used to model the plasma on an auroral magnetic field line and also to investigate how auroral acceleration can be simulated in a laboratory experiment (Gunell et al., 2013b). ...
... The magnetic moment is a constant of motion, and therefore we haveμ = 0. The Vlasov equation (Vlasov, 1938) that needs to be solved for our system is (Gunell et al., 2013a) ∂f ∂t ...
The plasma on an auroral field line is simulated using a Vlasov model. In the initial state, the acceleration region extends from one to three Earth radii in altitude with about half of the acceleration voltage concentrated in a stationary double layer at the bottom of this region. A population of electrons is trapped between the double layer and their magnetic mirror points at lower altitudes. A simulation study is carried out to examine the effects of fluctuations in the total accelerating voltage, which may be due to changes in the generator or the load of the auroral current circuit. The electron distribution function on the high potential side of the double layer changes significantly depending on whether the perturbation is toward higher or lower voltages, and therefore measurements of electron distribution functions provide information about the recent history of the voltage. Electron phase space holes are seen as a result of the induced fluctuations. Most of the voltage perturbation is assumed by the double layer. Hysteresis effects in the position of the double layer are observed when the voltage first is lowered and then brought back to its initial value.
... By virtue of flux conservation, this provides a measure of the upward ion flux at the altitude of the bottom of the acceleration region. This altitude is not precisely known yet; for discrete auroral arcs observations find it to be between ∼0.5 and ∼2 R E [see Karlsson, 2012, and references therein], with simulations showing that the altitude of the acceleration region depends on the energy: at higher altitudes for lower energies [e.g., Gunell et al., 2013]. For polar cap arcs, with potential drops on average an order of magnitude smaller than for auroral arcs, this will thus likely be around ∼1 R E altitude or higher. ...
We measure the flux density, composition, and energy of outflowing ions above the polar cap, accelerated by quasi-static electric fields parallel to the magnetic field and associated with polar cap arcs, using Cluster. Mapping the spacecraft position to its ionospheric foot point, we analyze the dependence of these parameters on the solar zenith angle (SZA). We find a clear transition at SZA between We find a clear transition at SZA between $\sim$94$^{\circ}$ and $\sim$107$^{\circ}$, with the O$^{+}$ flux higher above the sunlit ionosphere. This dependence on the illumination of the local ionosphere indicates that significant O$^{+}$ upflow occurs locally above the polar ionosphere. The same is found for H$^{+}$, but to a lesser extent. This effect can result in a seasonal variation of the total ion upflow from the polar ionosphere. Furthermore, we show that low-magnitude field-aligned potential drops are preferentially observed above the sunlit ionosphere, suggesting a feedback effect of ionospheric conductivity.
This chapter aims to give an overview regarding ion outflow in the auroral region, illustrated by recent observations and results. This topic covers a wide range of domains, including auroral acceleration processes, auroral dynamics, auroral arc morphology, and atmospheric erosion. Ion outflow involves coupling between the ionosphere, the magnetosphere, and the solar wind. The chapter starts with a brief description of the energization processes of ionospheric ions, from the upper ionospheric regions to the magnetospheric regions connected to the auroral zone at altitudes up to several Earth radii (RE). It then discusses the observational properties of auroral outflow, including their large-scale spatial distribution, their link with auroral forms, their statistical dependence on solar and geomagnetic activity, and their modulation by auroral dynamics at the timescale of substorms. The chapter ends with a discussion about the impact of auroral outflow on the global ionosphere-magnetosphere system.
The existence of parallel electric fields is an essential ingredient of auroral physics, leading to the acceleration of particles that give rise to the auroral displays. An auroral flux tube is modelled using electrostatic Vlasov simulations, and the results are compared to simulations of a proposed laboratory device that is meant for studies of the plasma physical processes that occur on auroral field lines. The hot magnetospheric plasma is represented by a gas discharge plasma source in the laboratory device, and the cold plasma mimicking the ionospheric plasma is generated by a Q-machine source. In both systems, double layers form with plasma density gradients concentrated on their high potential sides. The systems differ regarding the properties of ion acoustic waves that are heavily damped in the magnetosphere, where the ion population is hot, but weakly damped in the laboratory, where the discharge ions are cold. Ion waves are excited by the ion beam that is created by acceleration in the double layer in both systems. The efficiency of this beam-plasma interaction depends on the acceleration voltage. For voltages where the interaction is less efficient, the laboratory experiment is more space-like.
