Ion temperature gradient mode driven solitons and shocks

Abstract

Ion temperature gradient (ITG) driven solitons and shocks are studied in a plasma having gradients in the equilibrium number density and equilibrium ion temperature. In the linear regime, it is found that the ion temperature and the ratio of the gradient scale lengths, ηi=Ln/LT, affect both the real frequency and the growth rate of the ITG driven wave instability. In the nonlinear regime, for the first time we derive a Korteweg de Vries-type equation for the ITG mode, which admits solitary wave solution. It is found that the ITG mode supports only compressive solitons. Further, it is noticed that the soliton amplitude and width are sensitive to the parameter ηi=Ln/LT. Second, in the presence of dissipation in the system, we obtain a Burger type equation, which admits the shock wave solution. This work may be useful to understand the low frequency electrostatic modes in inhomogeneous electron-ion plasma having density and ion temperature gradients. For illustration, the model has been applied to tokamak plasma.

Heat flux effect in ηi-mode driven solitary and shock waves in electron-positron-ion plasma

“…The obtained linear and nonlinear dispersion relations are solved numerically for the purpose to show the visible effects of new terms on the considered mode. For qualitative behavior of the numerical analysis we use the data given in (Qamar et al, 2003;Davydova & Pankin 1998;Zakir et al, 2016), some of these are: m i = 1.67 × 10 −24 g, n e = 10 14 cm −3 , B = 1.4 × 10 4 G, T eo = 10 5 eV , T io = 0.1T eo , n po = 0.001n eo , T P o = 0.1T eo , η i = 2, c s = 10 6 cm/s, ion gyrofrequency ω ci = 10 4 rad/s, in new coordinates u = 10 6 cm/s and α = 0.1rad. Based on various derived relations of our study we here discuss the linear and the nonlinear outcomes of our work.…”

Ion Temperature Gradient Mode–Driven Solitary and Shock Waves in Electron-Positron-Ion Magnetized Plasma

“…In this section of our work, we discuss the numerical results based on our analytical calculations derived in Sections 2, 3, and 4. For linear and nonlinear numerical analysis, we use the following parametric data from [39,40] such that m i = 1.67 × 10 −24 g, n = 10 14 cm −3 , B = 1.4 × 10 4 G, T e = 10 5 eV , T i = 0.1T e , n p = 0.001n e , T P = 0.1T e , η i = 2, c s = 10 6 cm/s, ion gyrofrequency ω ci = 10 4 rad/s, in new coordinates u = 10 6 cm/s, and α = 0.1rad. Figure 1 represents the linear plot of the phase velocity of the mode based on (15).…”

“…Frojdh et al [37] and Shukla and Stenflo [38] reported that the presence of several ions in magnetically confined devices such as tokamak (laboratory level) and in space and astrophysical plasmas modify the existing modes, e.g., in electron-ion plasma ITG mode can excite the zonal flows. Zakir et al [39] recently studied the ITG mode solitary and shock waves structures for the first time. According to our best knowledge, the ITG modedriven solitary and shock waves have not been studied earlier.…”

Formation of solitons and shocks in toroidal ion temperature gradient mode in the presence ofnon‐Maxwellianelectrons

“…Although ion temperature gradient (ITG)-driven modes can be found in both space and laboratory plasmas, however, their significance with regard to the anomalous transport of particles and energy in Tokamak is the major reason of interest in these modes. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] Many theoretical and experimental studies have confirmed that unwanted transport of particles in Tokamak is linked with 𝜂 i mode-driven instabilities. [5,6,[14][15][16] Here 𝜂 i = d ln T i d ln n i is defined as the ratio of scale length of ITG and ion density gradient.…”