4) Magnetic confinement of plasma
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1 4) Magneti onfineent of plasa Due to the shielding in the plasa, thee is alost no ontol with eleti fields. A ontol is possible with agneti fields, as patiles ae bound to the field lines. This is alled plasa onfineent. It is of fundaental inteest fo the agneti onfineent fusion (Tokaak, Stellaato). Exaple in natue: Guidane of High enegeti patiles of the osi adiation by the eath agneti field to the poles geneation of pola lights. WS011/1 4.1
2 We solely take single patile otion in the agneti field into aount. If we inlude olletie effets, we need agneto hydodynaik (MHD) theoy. Loentz foet: & yields & 0 L L As, the agneti field has no influene on the otion paallel to the agneti field. The dietion of the eloity hanges pependiula to the agneti field, hene the kineti enegy of the patiles is onstant (obit otion). ω ω ω yloton feueny (4.1) ω e 11 e [ Hz] [ T ], ωi ωe i, WS011/1 4.
3 Radius on obit: Gyation of eletons Plasa diagnosti Injetion of an eletoagneti wae of ω ω e plasa heating Using 1 kt ( degees of feedo pependiula to ) the Lao adius L is L kt T e [ ev ] [ ] T [ ] (4.) Exaple: T e 1 ev, 1 T L 3.4 µ Let s now inestigate & Assuing an additional foe ating on the patiles no losed obit WS011/1 4.3
4 WS011/1 4.4 o onstant und in tie and spae guiding ente-ansatz The ente otion is alulated ia g g, The eloity of the guiding ente is gie by g & & & & ) ( 1 with ) ( ) ( the following esult of the otion is deied and & (4.3) The seond te is alled dift eloity. This te does not aeleate and is dieted pependiula to and.
5 Exaples: 1.) elekti field E E x dift E D The dift eloity is not dependent on the hage of the patile..) Gaitation g The patile gains enegy in the dietion of sepaation intoduing the uent Ex-dift in dietion of the x-axis. The gyation adii ae not dawn to sale! g D g. The dift is hage dependent and leads to a hage g i e( i e) nee e Z jg ne e o soues this dift is negligible. Moe ipotant ae difts due to gadients. WS011/1 4.5
6 3.) -Dift, if f ( x, t) uatue dift Due to 0 a gadient in leads to a uatue of the field lines. This esults in a entifugal foe ˆ D R ˆ ˆ dt R ds ˆ R. The entifugal foe is in dietion of D and hene 3 Patile dift in a tooidal agneti field. The dift esults in a hage sepaation and the esulting Ex-dift oes the plasa outwad Exaple: tooidal agneti field WS011/1 4.6
7 WS011/1 4.7 Adiabati inaiane of the agneti oent A haged patile on a iula obit eates a uent in the agneti field. π ω π I agneti dipole oent: L L n n n I n d I 1 ω µ Assuing the Lao adius L W µ (4.4) How does the agneti oent hange with a slow dift of the guiding ente? Change of the agneti flux φ though the obit aea! Gyation peiod C ω π τ and d d W L π φ d d W dw L µ τ π τ if τ and L ae intodued.
8 On the othe hand dw d dµ d ( µ ) µ dµ hene: 0, µ onst. The agneti oent is onstant unde a slow dift of the guiding ente (slow in opaison to the obit otion). Exaple: adiabati inaiant agneti io If a haged patile oes into a zone with stonge agneti field, the kineti enegy of the gyation ineases due to the inaiane of the agneti oent. As the total kineti enegy in of the patile does not hange (no ollisions) the kineti enegy in Dietion of the guiding ente otion ust be edued. In ode to edue opletly µ ( W ax 1 ) W W W1 >,1 The patile stats at position 1 between the oils. At Pos. is the axiu of the agneti field ax. WS011/1 4.8
9 ( ),1 1 1 ot 1 W W 1 / 1 is alled io atio. W W W 1 α W1 1 W1 W1 1 α 1 1 The loss on eis haateized by α asin( in ax ) (4.5) This euation deonstates that a agneti io is not pefet. Patiles with sall eloity oponents pependiula to the agneti field ae not efleted, but slowed down (as thei angles towads the axis ae salle then α). WS011/1 4.9
10 Patile otion within the eath agneti field. At the pola egions agneti ios exist and the uatue dift lead to an euatoial uent. Magneti onfineent is used in the field of ion soue in Eleton Cykloton Resonanz Ion Soue (ECRIS) (esonane heating of plass using f) Confineent of ions in an Eletone ea Ion Soue (EIS) Multiusp-Ion Soues Motion of ions in an EIS o a Penning tap WS011/1 4.10
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