Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
Chapter 4 SINGLE PARTICLE MOTIONS 4.1 Introduction
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
4.4 Inhomogeneous Fields 113Passing orbitsAs the particle moves freely toroidally, its orbit projected onto the R-z (poloidal)plane is given bydxdt = −Ωz dzdt =Ωx + v z (4.93)wherewehavetakenx = R − R 0 and where the vertical z drift velocity is givenbyv z =m2qB φ R (2v2 ‖ + v2 ⊥ ). (4.94)In Eq. (4.93) Ω = dθ/dt is the angular velocity of the particle orbit projectedonto the poloidal plane (imagine the torus straightened into a cylinder and lookingalong the axis of the helical magnetic field line). The rotation in this plane arisesfrom the helicity of the magnetic field line. The rate of spiralling of the field lineis given byrdθB θ= RdφB 0and is characterised by the so-called winding number or safety factor q(r) whichis defined byq(r) = dφdθ = rB 0= ɛ B 0. (4.95)RB θ B θIn tokamaks, q typically lies in the range 0.7
Change language