Tham khảo tài liệu 'crc press - dictionary of material science and high energy physics - d. basu (2001) episode 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | where A is the amplitude a p are constants t is the time and x is the position. Hence as the amplitude increases the speed increases while the width shrinks. Solitons are related to shock waves through a quasi-potential called the Sagdeev potential. ion acoustic wave The only normal mode of ions allowed in nonmagnetized plasmas ion acoustic waves are essentially driven by thermal motions of both electrons and ions. In fact their phase and group velocities are given by the ion acoustic or sound speed cs KTe 3KTi mi 1 2 where K is the Boltzman constant Te and Ti are the electron and ion temperatures and mi is the ion mass. With the use of the ion acoustic speed the dispersion relation of the ion acoustic wave with frequency ờ and wave number k is given by ờ kcs. There are two damping mechanisms for ion acoustic waves one is Landau damping and the other is the non-linear Landau damping that occurs after trapping of particles inside the electrostatic wave potential of relatively large ion acoustic waves. Ion acoustic waves are heavily damped if Te T so that such waves usually propagate only in plasmas with T Te. Various non- linear states of ion acoustic waves have been the subjects of intensive research in plasma physics for many years. As they are amplified these waves may form solitons double layers and shock waves. See also ion wave. ion beam instabilities There are several instabilities driven by an ion beam which in a magnetized plasma usually propagates along an external magnetic field. Electrostatic instabilities are the ion acoustic instability driven by the relative drift between the electrons and the beam ions and the ion-ion drift instability. The former generates principally field-aligned waves and the latter generates either field-aligned or oblique waves. Among electromagnetic instabilities are the ion-ion resonant and nonresonant instabilities the former excite right-hand circularly polarized waves and the latter excite lefthand circularly polarized .
