B B≈0 In=B where n is the number of turns Thus The magnetic field also has the essential property of being solenoidal, i.e V.B=0 (notice that, due to Ampere's law, j also obeys vj=0, which can be seen as a statement of charge conservation). In regions where no current is flowing we have VxB=0 as well, so that a magnetic potential can be defined by B=-Vy. Then, since VB=0, this potential obeys Laplace's equation (19) but notice that Ich potential exists in a current-carrying plasma. The vector B there must be found by simultaneous solution of Ampere s and ohms laws(with the additional constraint V B=0) Consider now a conductive plasma inside a solenoid, so that both an external B field (Bext)and an induced B field(Bindexist. The first is due to the coil currents, the second to those in the plasma itself. Suppose the plasma currents are due to the 16.522, Space P pessan Lecture 21 Prof. Manuel martinez Page 7 of 2116.522, Space Propulsion Lecture 21 Prof. Manuel Martinez-Sanchez Page 7 of 21 0 B I n = l µ JG where n is the number of turns. Thus 0 n B= I l µ . The magnetic field also has the essential property of being solenoidal, i.e., ∇. B = 0 JG (18) (notice that, due to Ampère’s law, j G also obeys ∇. j = 0 G , which can be seen as a statement of charge conservation). In regions where no current is flowing we have ∇ × B = 0 JG as well, so that a magnetic potential can be defined by B=-∇ψ JG . Then, since ∇. B = 0, JG this potential obeys Laplace’s equation 2 ∇ ψ = 0 (19) but notice that no such potential exists in a current-carrying plasma. The vector B JG there must be found by simultaneous solution of Ampère’s and Ohm’s laws (with the additional constraint ∇. B = 0 JG ). Consider now a conductive plasma inside a solenoid, so that both an external B JG field ( ) Bext JG and an induced B JG field ( ) Bind JG exist. The first is due to the coil currents, the second to those in the plasma itself. Suppose the plasma currents are due to the