By Valentin Igochine
During the previous century, world-wide strength intake has risen dramatically, which ends up in a quest for brand spanking new strength resources. Fusion of hydrogen atoms in sizzling plasmas is an enticing method of remedy the strength challenge, with considerable gas, inherent security and no long-lived radioactivity. besides the fact that, one of many limits on plasma functionality is because of many of the sessions of magneto-hydrodynamic instabilities which could happen. The physics and keep an eye on of those instabilities in sleek magnetic confinement fusion units is the topic of this e-book. Written via top-rated specialists, the contributions will offer worthy reference and up to date examine stories for "old fingers" and novices alike.
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Additional resources for Active Control of Magneto-hydrodynamic Instabilities in Hot Plasmas
0Þ, otherwise the plasma is unstable ðdW \ 0Þ. It is convenient to write this equation in the so-called ‘‘intuitive form’’ [8, 11]. dW ¼ dWplasma þ dWvacuum þ dWsurface dWplasma ¼ Z 1 2 plasma ð2:35Þ ( 2 2 2 ~ B1;? B2 j Á~ nÃ? n? þ 2~ n? Á ~ j þCp0 r Á ~ n À2 ~ n? Á rp0 ~ þ 0 r Á ~ l0 l0 É ^ nÃ? Â ~ b Á~ B1;? dV À Jk ~ dWvacuum ¼ 1 2 Z vacuum 1 ¼ 2 dWsurface Z surface ðB 1 Þ2 dV l0 B2 ~ 2 dS n Á n? ~ nÁ r p þ ~ 2l0 l ^ ^ ~ B1 ¼ ~ n Á rp0 ; ~ B1;?
The prime indicates differentiation with respect to À W. Á The right side of the equation is proportional to the toroidal current density J/ . The functions WðR; zÞ and I ðR; zÞ are connected to the plasma current density ðJ Þ and the magnetic field as follows: BR ¼ À 1 oW 1 oW 1 oI 1 oI Bz ¼ JR ¼ Jz ¼ À R oz R oR R oz R oR ð2:20Þ The Grad-Shafranov equation can be solved numerically for any plasma crosssection and provides the constant flux (and pressure) surfaces in real tokamak geometry. Detailed derivation of the equation can be found, for example, in the book by J.
Thus, the safety factor value of the resonant surface follows directly from the helical structure of the instability ðq ¼ m=nÞ. 30). It is called ‘‘linear growth’’ phase. This description is applicable only in some special cases, for example for resistive wall modes dynamic in RFPs. In practice, the modes are often in non-linear regime and this assumption is not valid anymore, for example for tearing modes, edge localized modes, etc. 2 Magneto-Hydrodynamics and Operational Limits 29 rotates with respect to the laboratory frame, its rotation is characterized by the mode frequency ðxÞ.