A magnetic field B is found to be convected by the electron heat flux cf e because of the Nernst effect, i.e., with a velocity V T ( ~ 2^e/3n e T e ). In laser-driven ablation the convection is towards the overdense region and B can be amplified by 10-100 times because V • V T < 0, making B/n t and hence o) e r e almost constant for X mfp > c/w^. The spatially extended and amplified magnetic field can inhibit hot-electron transport, reducing preheat. For o) e T e > 1, the critical and ablation surfaces are brought closer together, which increases hydrodynamic coupling. PACS numbers: 52.25.Fi, 44.90. + c, 47.65.Fi In laser-driven fusion, uniform implosion is one of the key issues for successful performance. Among the sources of nonuniformity, an irradiation asymmetry has been believed to be smoothed out by electron thermal conduction. 1 But the inclusion of a self-generated magnetic field may change the situation. Several sources of such a magnetic field have been reported by many authors. 2 "" 9 In Refs. 2 and 3, the magnetic field is generated near the ablation region and in the others generated around the critical density.If we take no account of the effects of the thermal force, these magnetic fields are convected towards the underdense region by fluid flow. The most important point in considering the effect of a magnetic field is not where it is generated, but where it exists. In this context, the magnetic field transport becomes a critical issue. Some properties of the Nernst term have been suggested by earlier authors. Dolginov and Urpin 10 mentioned in their paper that the magnetic field will be convected to lower-temperature regions. Parfenov and Shishko 11 have shown that the transverse magnetic field profile in a magnetohydrodynamic shock is strongly affected by inclusion of the Nernst effect.In this Letter, we discuss the effect of the thermal force on the magnetic field transport and amplification, and we show that a magnetic field is transported to the overdense region by the electron heat flux. Furthermore we show that the magnetic field grows in magnitude to a value that is decided by the balance between convection and diffusion.To discuss these effects, we use the magnetohydrodynamic equations, which consist of conservation of mass, momentum, and energy, with the effect of the magnetic field as given by Braginskii. 12 The equation for the magnetic field is dt e n e 4ire Vx (VxB)xB -Vx IV7 , "T" IVW(1)where B, w, n e , P e , R T , and R u are the magnetic field, the ion velocity, the electron number density, the electron pressure, the thermal force, and the frictional force, respectively. The coupled partial differential equations described above are solved by our newly developed fluid particle-in-cell code 13 in one-or twodimensional plane geometry. Before presenting the detailed simulation results, let us analyze the thermal force term in the equation for the magnetic field. The fourth term in Eq. (1) can be rewritten as -Vx ft uT •vr, + v -B P'{X l + N m 0 VT P + V ca i ATrn}e 2 V5 + Vx c 2...
The nonlinear stationary states of an electron beam moving in a homogeneous positive background are calculated for the full range of amplitudes Em of a longitudinal self-induced electric field in the collisionless limit. The parameter that controls the system is κ=Em/(4πn0mev02)1/2, where n0,v0 are the number density and velocity of the beam when electrons are submitted to maximum force. If κ≪1 the beam variables vary harmonically in space. As κ increases within 0<κ⩽1, the beam variables become gradually anharmonic but their wavelength remains constant and independent of κ. If κ>1 it is shown that no wave breaking occurs. Instead, the electric field becomes discontinuous at certain points and the electrons delay there forming periodic electrostatic (Langmuir) structures centered around negatively charged planes. The size and charge of the above structures as well as their wavelength, which now depends on κ, are derived.
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