See Also: grad-shafranov equation(medicine)
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grad-shafranov equation (medicine) and Proper (medicine)


grad-shafranov equation (medicine)


grad-shafranov equation
<radiobiology> Reduced magnetohydrodynamic-equilibrium equation for an axisymmetric, toroidal plasma. (Similar reduced equations can be derived for the cases of helical symmetry and for the straight cylinder.)

Analytic and numerical studies of these equations are important in exploring potential plasma configurations. The lowest order force balance in the plasma is simply that the Lorentz force must be balanced by the pressure force. This balance, combined with Maxwell's equations, determines the equilibrium configuration of the magnetic field.

When the toroidal configuration is axisymmetric, and the equilibrium plasma flow is zero, the magnetic field may be written in terms of a stream function psi that satisfies the Grad-Shafranov equation Deltapsi = - mu_0 R^2 p'(psi) - FF'(psi). Here p is the plasma pressure and f = R B_phi. (R is the radial distance from the axis of the machine).

In an axisymmetric torus, in the absence of equilibrium plasma fluid flows, the magnetic field may be written in terms of a scalar potential. When the plasma is in equilibrium (forces balance and the plasma is stationary), this scalar potential obeys a non-linear elliptic equation known as the Grad-Shafranov equation.


Proper (medicine)


proper


1. Belonging to one; one's own; individual. "His proper good" [i. E, his own possessions] . "My proper son." "Now learn the difference, at your proper cost, Betwixt true valor and an empty boast." (Dryden)

2. Belonging to the natural or essential constitution; peculiar; not common; particular; as, every animal has his proper instincts and appetites. "Those high and peculiar attributes . . . Which constitute our proper humanity." (Coleridge)

3. Befitting one's Nature, qualities, etc.; suitable in all respect; appropriate; right; fit; decent; as, water is the proper element for fish; a proper dress. "The proper study of mankind is man." (Pope) "In Athens all was pleasure, mirth, and play, All proper to the spring, and sprightly May." (Dryden)

4. Becoming in appearance; well formed; handsome. "Thou Art a proper man." "Moses . . . Was hid three months of his parents, because they saw he was a proper child." (Heb. Xi. 23)

5. Pertaining to one of a species, but not common to the whole; not appellative; opposed to common; as, a proper name; Dublin is the proper name of a city.

6. Rightly so called; strictly considered; as, Greece proper; the Garden proper.

7. Represented in its natural colour; said of any object used as a charge. In proper, individually; privately.

<botany> Proper flower or corolla, a receptacle which supports only a single flower or fructification.

Origin: OE. Propre, F. Propre, fr. L. Proprius. Cf. Appropriate.

Source: Websters Dictionary