| | 276 | The 2-D Harris current sheet test can be set up as follows:[[BR]][[BR]] |
| | 277 | [[latex($B_y(x) = b_0 tanh(x/a)$)]][[BR]][[BR]] |
| | 278 | where in computational units we choose [[latex($b_0 = 1$)]] and [[latex($a = 0.5$)]].[[BR]] |
| | 279 | The density profile is chosen so that the pressure equilibrium can be maintained with constant temperature.[[BR]][[BR]] |
| | 280 | [[latex($\rho(x) = \rho_0/cosh^2(x/a)+\rho_c$)]][[BR]][[BR]] |
| | 281 | where [[latex($\rho_0 = 1$)]] and [[latex($a = 0.5$)]]. The temperature is set to be constant as 0.5. [[BR]] |
| | 282 | The domain is set to be -6.4 < x < 6.4 and -12.8< y < 12.8, with fixed resolution 480 * 960. The boundaries are all open.[[BR]] |
| | 283 | The initial state is in pressure equilibrium though unstable. We put in a perturbation: [[BR]][[BR]] |
| | 284 | [[latex($\B_x = B_p sin(kx)cos(ky)$)]][[BR]] |
| | 285 | [[latex($\B_y = -B_p cos(kx)sin(ky)$)]][[BR]][[BR]] |
| | 286 | where [[latex($\B_p$)]] is the perturbation amplitude and [[latex($k = 2\pi/L_y$)]]. |
| | 287 | The magnetic field and the density profiles are plotted below:[[BR]][[BR]] |
| | 288 | |
| | 289 | The magnetic energy is diminished at the X point which will convert to bulk ram pressure that drives the y direction outflow around the x = 0 line. [[BR]] |
| | 290 | For the outflow pattern, the leading edge is bounded by intermediate shocks and the trailing edge is bounded by slow shocks. There are totally four slow mode shocks stemming from the Sweet-Parker region, as shown in the following figure.[[BR]][[BR]] |
| | 291 | |
| | 292 | The time evolution model can be given by the Semenov solution.[[BR]] |
| | 293 | |
| | 294 | |
| | 295 | |
| | 296 | Other possible tests:[[BR]] |
