Proper Frame Determination and Walen Test
Abstract
To study structures, such as current sheets, flux ropes, or fully three-dimensional configurations, it is desirable to examine them in their proper (co-moving) frame, in which they appear as time stationary as the data permit. And it is important to establish the frame velocity so that their physical dimensions can be determined. In the present chapter, we discuss methods for finding the velocity of the proper frame, mostly from single spacecraft data. The so-called Walen test is also discussed in the chapter. Its purpose is to identify one-dimensional Alfvenic structures from single-spacecraft data, usually in the context of magnetic field reconnection geometries or interplanetary discontinuities.
The simplest situation is one where the electric field in the proper frame is negligibly small. When such is the case, the co-moving frame is called the de Hoffmann-Teller (HT) frame. It was first applied by de Hoffmann and Teller [1950] in a theoretical study of the one-dimensional structure of MHD shocks. In this application, the HT frame was specified by the requirement that the electric field on both sides of the shock, but not necessarily in the middle of it, was zero. In other words, the plasma flow on the two sides was field- aligned, when viewed in the HT frame. The component of the frame velocity, V HT, along the direction normal to a one-dimensional layer represents the motion of the layer, while the tangential component represents what has been called the field-line velocity. Important applications of the HT frame include the study of particle reflection and acceleration at shocks (see Section 8.2.1), at the magnetopause, and in the geomagnetic tail current sheet. It is also used in the Grad-Shafranov reconstruction methods presented in Chapter 9. The concept of an HT frame is not limited to one-dimensional structures. Such a frame can exist for some two- and three-dimensional objects as well. But there are also structures which possess an intrinsic electrostatic field that cannot be transformed away . An example is the standard two-dimensional reconnection configuration, which, in its proper frame (the frame moving with the X-line), has a remnant electric field along the invariant (axial) direction. Determination of the magnitude of this reconnection-generated field is an important goal. To reach it, a high-quality determination of the proper frame is required.The procedure, first developed in Sonnerup et al. [1987], for obtaining the HT frame velocity and, if so desired, its acceleration, from data measured by a single spacecraft was described in Chapter 9 of ISSI SR-001 [Khrabrov and Sonnerup, 1998]. Comments on the procedure and applications are given in Section 7.2 below. The more general situations, in which no HT frame exists, i.e., where the structures have an intrinsic remaining electrostatic field in their proper frame are discussed in Section 7.3.- Publication:
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ISSI Scientific Reports Series
- Pub Date:
- 2008
- Bibcode:
- 2008ISSIR...8...65P
- Keywords:
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- space plasmas;
- proper frames;
- de Hoffmann-Teller frame