# Minardi, E. Thermodynamics of High Temperature Plasmas. Entropy, 2009, 11, 124-221

^{th}line from below:

**selects**the …

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**plays**…

**when the plasma is stationary (**$\partial {\overrightarrow{j}}_{p}/\partial t=0$

**).**

^{th}line from above:

**assuming for simplicity the absence of the sawteeth zone ($C=0$), Equation (8.4) becomes**…

^{th}line from above:

^{th}line from above up to Table I included:

_{0}is the value of the safety factor on the minor axis, $j\left(\lambda \right),j\left(1\right)$ are the values of the current density at the inner and outer border respectively, and $\left|\tau \right|\Delta {S}_{p}$ given by (9.7) is the electromagnetic energy released by the collective system when the electromagnetic entropy increases.

_{0}, which fact explains why a sawteeth zone with q

_{0}< 1 is always formed in tokamaks (unless the sawteeth are contrasted by some external action).

**Table I.**Meaning of symbols: Δψ, variation of the poloidal flux (divided by 2π); q

_{0}, safety factor on magnetic axis; j(λ),current density on the q = 1 surface; j(1), current density at the outer border of the relaxed region; $\Delta {\Phi}_{\text{int}}$, electromagnetic energy released associated with the magnetic entropy increase ΔS

_{p}.

Δψ T − m ^{2} | q_{0} | j(λ) MA/m ^{2} | j(1) MA/m ^{2} | $\left|\tau \right|\Delta {S}_{p}$ MJ |
---|---|---|---|---|

0.00 | 0.98 | 1.72 | 0.022 | 0.00 |

-0.017 | 0.92 | 1.62 | 0.057 | 0.030 |

-0.038 | 0.87 | 1.52 | 0.088 | 0.059 |

-0.051 | 0.81 | 1.41 | 0.12 | 0.090 |

-0.063 | 0.77 | 1.34 | 0.15 | 0.11 |

**loss of the poloidal flux**”

_{p}

**(where S**

_{p}is given by (6.3)):**(10.5)**and...

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**sections**”.

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**Section**1”.

_{0}(the safety factor in the sawteeth region is modeled according to (9.11)), on the position λsa of the q = 1 surface, on the parameter μa and on the value of the current density at the outer border of the relaxed region. The average values of q

_{0}and of λsa are determined by the dynamics of the sawteeth in the zone q < 1. Thus we keep these parameters as fixed and calculate w as function of μa keeping fixed also the total current, while the current density at the border is varying. One finds that w decreases when μa decreases, while the current density at the border increases. Both quantities reach asymptotically a constant value for μa → 0. Therefore the limiting process μa → 0 with constant total current minimizes the poloidal magnetic energy (17.1). This fact is at the root of the profile consistency of the SME states (the term “profile consistency” has been used for the first time by Coppi).

**includes**the Poynting flux..

_{0}is the same as in (16.3),

**as required by consistency with the power balance**. Thus,

**recalling (7.2), the heat flux across the surface**S = 4π

^{2}rR

**becomes (neglecting non inductive currents)**

**The heat flux is continuous across the surface**$\widehat{q}=1$ (we note that…

_{0}+ (1 − q

_{0})(x/λ)

^{2}for the safety factor..

_{eff}) should be corrected as follows:

_{eff}) = 1.9745· 10

^{−31}Z

_{eff}

_{0}= j

_{0}q

_{0}β

**..**

**is Maxwellian**with local temperature T

_{j}in each ΕV

_{j}…

## References and Notes

- Minardi, E. Thermodynamics of High Temperature Plasmas. Entropy
**2009**, 11, 124–221. [Google Scholar] [CrossRef]

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Minardi, E.
Minardi, E. Thermodynamics of High Temperature Plasmas. *Entropy*, 2009, *11*, 124-221. *Entropy* **2009**, *11*, 457-462.
https://doi.org/10.3390/e11030457

**AMA Style**

Minardi E.
Minardi, E. Thermodynamics of High Temperature Plasmas. *Entropy*, 2009, *11*, 124-221. *Entropy*. 2009; 11(3):457-462.
https://doi.org/10.3390/e11030457

**Chicago/Turabian Style**

Minardi, Ettore.
2009. "Minardi, E. Thermodynamics of High Temperature Plasmas. *Entropy*, 2009, *11*, 124-221" *Entropy* 11, no. 3: 457-462.
https://doi.org/10.3390/e11030457