Observations

Global observations of energy transfer or conversion at the magnetopause is diffi-cult given the little satellite coverage of the magnetopause. However, it is possible to estimate energy converted locally during a magnetopause crossing from in situ observations. Wright [1996] has formulated basic MHD theory to estimate the tan-gential stress at the magnetopause as a result of large scale convection pattern set up by reconnection. Recently, Rosenqvist et al. [2006] presented the local energy conversion estimates from Cluster measurements during a magnetopause crossing.

They have used the following equation to calculate the converted energy during the crossing

Q(W m⁻²) = )

{(J×B)·V} |Vmp|dt (1.5) whereJ is current density, B is magnetic field,V is the plasma velocity and Vmp

is the magnetopause velocity in the normal direction. In a time-independent case, it is straightforward to show that J×B·V equals E·J which in turn is equal to Eq. 1.3. Notice that |Vmp|dt = dl, represents integration over the width of the magnetopause. The magnetopause velocity Vmp can be positive or negative but in the energy conversion computation only the absolute value matters. This is because physically the sign of the energy conversion should be determined by J×B·V and not the magnetopause velocity, which is only used to convert the spatial integration measure into temporal form. Rosenqvist et al. [2006] found that the energy conversion can be milliwatts per unit area locally during a major magnetic storm, and using this value they also obtained a crude estimate for the total energy transfer by making assumptions on the energy transfer spatial distribution at the magnetopause. Note that the length of the integration path does not affect the final out come as most of the energy conversion takes place in the magnetopause current layer. On either side of the magnetopause the energy conversion is negligible and does not change the final outcome.

Further, Rosenqvist et al. [2008a] calculated energy conversion using Eq. 1.5 from a series of Cluster magnetopause crossings which occurred during 2001-01-26. These magnetopause crossings have been widely studied and confirmed that continuous reconnection is ongoing [Bosqued et al., 2001; Phan et al., 2004]. Rosenqvist et al.

[2008a] calculated reconnection rate during a set of 11 magnetopause crossings and concluded that the reconnection is continuous but the rate is modulated. They used both single and multispacecraft methods to estimate magnetopause orientation, velocity and current density along with magnetopause orientation also from the Shue et al. [1998] model. In another study, Rosenqvist et al. [2008b] presented a comparison of local energy conversion estimated during two magnetopause crossings with BATSRUS MHD simulation [Gombosi et al., 2002, Powell et al., 1999] results.

The results from simulations and Cluster observations in these two events agree in sign after artificially lowering the Cluster latitude at the magnetopause. Figure 1.7

28 CHAPTER 1. INTRODUCTION indicates that this artificial move can move the spacecraft from a generator area to a load area, also changing the sign of energy conversion. This procedure indicates that computing energy conversion from spacecraft observations may be sensitive to a number of uncertainties.

Paper IandPaper IIpresented comparison of two magnetopause crossings by Cluster spacecraft with GUMICS-4 simulations. One of the magnetopause cross-ing presented in Paper Iwas a load magnetopause crossing while the other was a generator crossing. Both magnetopause crossings presented inPaper IIare genera-tors. Both these papers used multispacecraft methods to estimate the magnetopause normal, velocity and current density and later the converted energy from Eq. 1.5.

Paper III presented energy conversion estimates during 27 Cluster high latitude magnetopause crossings which used both multispacecraft methods as well as single spacecraft methods. The main point ofPaper III was to investigate the influence of magnetopause normal, velocity and current density on the calculation of energy conversion and to compare single spacecraft estimates with the multispacecraft es-timates. Another major idea of Paper III is to establish the error bars in single spacecraft energy conversion estimates. Paper IV investigated energy conversion at the magnetopause using a database of about 4000 magnetopause crossings using single spacecraft methods and the goal of this paper is to investigate the spatial vari-ation of magnetopause energy conversion suggested by simulvari-ations [Laitinen et al., 2007].

Chapter 2

IMF control of energy conversion

Early spacecraft and ground based observations on the occurrence of magnetospheric substorms and storms suggested that these phenomena depend on the IMF direc-tion especially the north-south (Z) component of IMF [Fairfield, 1967, Fairfield and Cahill, 1966, Nishida, 1968, Rostoker and Fälthammar, 1967]. The classic paper on magnetospheric convection by Dungey [1961] suggests that when IMF is purely southward, interplanetary and terrestrial magnetic fields merge on the dayside and the terrestrial field lines thus opened by magnetic field reconnection convect towards the nightside over the poles. This picture of magnetospheric convection and recon-nection between IMF and the terrestrial field was later corroborated using satellite measurements [Paschmann et al., 1979, Sonnerup et al., 1981].

According to Dungey’s [1961] picture for purely southward IMF, the magnetic field lines opened by reconnection convect symmetrically to the magnetotail. How-ever, IMF is seldom purely southward or northward. Both IMF X and Y components exert a stress on the open magnetic field lines and change their dynamics consider-ably. For example, the dawn-dusk IMF component applies a stress on the open field lines in the dawn and dusk directions such that a torque pulls the opened field lines asymmetrically to the magnetotail [Cowley, 1981, Fairfield, 1979, Tsurutani et al., 1984]. Cowley et al. [1991] presented an explanation of the observed asymmetries of the flows (see Fig. 2.1). The asymmetrical evolution of open flux to the magnetotail applies asymmetric inward forces on the closed magnetospheric field lines, which induce a perturbed magnetic field that has the same sense as the direction of IMF Y-component. This perturbed magnetic field Y-component sets up asymmetries in the cusp location [Newell et al., 1989], auroral oval location [Holzworth and Meng, 1984], and particle precipitation [Candidi et al., 1983].

Figure 2.1 presents some of the asymmetries caused by the partial penetration of IMF Y-component into the magnetosphere in the northern hemisphere for both positive (Fig. 2.1(a)) and negative (Fig. 2.1(b)) IMF Y-component. The dotted line representing the open closed field line boundary is shifted towards dawn when IMF Y is positive and towards dusk when IMF Y is negative. In the southern hemisphere the opposite effect occurs. This asymmetry in the open closed field line boundary is also observed from the ground based observations. The size of the auroral oval is an indicator of the open flux content in the magnetosphere and hence a good marker of the reconnection rate. Since the open flux is transported asymmetrically the size of

29

30 CHAPTER 2. IMF CONTROL OF ENERGY CONVERSION

Figure 2.1: Ionospheric consequences of the asymmetric evolution of open flux tubes at the magnetopause that depend on the dawn-dusk component of IMF. The solid curves are the flow stream lines and the dashed line is the open-closed field line boundary. The circles with dots indicate field-aligned currents that are going up to the magnetosphere and those with crosses are the field-aligned currents coming down into the ionosphere. All these three features show a dawn-dusk asymmetry that is caused by the dawn-dusk component of IMF (Figure Adapted from Cowley et al. [1991]).

the auroral oval is also asymmetric with respect to the noon-midnight meridian [e.g.

Candidi et al. [1983]]. This asymmetry is explained by the latitudinal displacement of the closed field lines [Cowley et al., 1991].

When IMF Y-component is positive (negative), the centre of the flow across the open and closed field lines shifts to the dusk-side (dawn-side) in the northern hemisphere and vice versa in the southern hemisphere. The cusp maps to the open and closed field line boundary on the dayside and from Fig. 2.1 an asymmetry in the cusp location is expected. The cusp asymmetry due to the IMF Y component was studied by Newell et al. [1989]. Corresponding asymmetries in auroral precipitation were reported recently [Farrugia et al., 2004, Newell et al., 2004, Sandholt et al., 2004].

The location of magnetopause reconnection and the resulting tailward flux

trans-2.1. VERIFICATION OF SIMULATIONS: OBSERVATIONAL SETUP 31 port play decisive roles when determining energy conversion and transfer. In the presence of a non-zero IMF Y-component, the magnetopause reconnection line is tilted away from the ecliptic. Cooling et al. [2001] presented a model that describes the reconnection line location and the subsequent evolution of the open field lines.

As the energy transfer occurs through advecting open field lines, the energy transfer and conversion should also display an asymmetry.

Global energy transfer results [Palmroth et al., 2006a] from simulations suggested that majority of the energy is transferred in the plane of the IMF clock angle thus exhibiting an asymmetry due to the IMF Y component. Further, simulation results on local energy conversion [Laitinen et al., 2007] showed a spatial variation which also depends on the IMF clock angle. Laitinen et al. presented a clear boundary between the load and generator regions during southward IMF, showing the characteristic asymmetry dependent on IMF Y-component.

2.1 Verification of simulations: Observational setup

Observational verification of global energy transfer results of Palmroth et al. [2003, 2006a] is challenging. However, it is possible to consider the suggestion that majority of the energy is transferred through the magnetopause in the plane of the IMF clock angle while other sectors should observe lower energy transfer. Simultaneous observation of this needs a spacecraft placed in the plane of the clock angle and another somewhere away from the clock angle, both crossing the magnetopause simultaneously. Given the rarity of spacecraft conjunctions at the magnetopause, one must use several events with controlled driver conditions and have the spacecraft sampling the magnetopause in the same region of space. If there is a spatial variation in energy conversion, a spacecraft crossing the magnetopause in the same sector as the IMF clock angle should record more energy conversion than a spacecraft outside the IMF clock angle sector.

Figure 2.2 illustrates this idea clearly using two IMF clock angles that differ in the sign of the Y component. If, the spacecraft is traversing the magnetopause in the same location in the northern dusk (yellow shaded region in Fig. 2.2) then an event during IMF Y negative (Fig. 2.2b) should see energy transfer while the other event having a positive IMF Y component should not.