which is non-negative every where.
In recent years, people have found that tokamaks often show improved confinement when the
magnetic shear in the central region is reversed.
Reversed magnetic shear represents a major modification of the usual q profile, with a
high central q value and non-monotonic q(r) achieved by delibrate modification of plasma
start up conditions.
See figure 14 for q profiles in traditional and reversed shear plasmas. 
Figure 1: q profiles of traditional and reversed shear plasmas
We have to start from Grad-Shafranov equation, bootstrap current before talking
about reversed magnetic shear.
Grad-Shafranov Equation
Grad-Shafranov equation is a reduced equilibrium equation for an axisymmetric toroid:
where 
is the ploidal flux, R, 
and Z form a cylindrical coordinate system
based on major axis, p is pressure, 
.
The equation is a non-linear second order partial differential equation which in general
has to be solved numerically. For derivation of Grad-Shafranov equation and others see
[4] Bateman pp.66-70.
20 years ago A. Sykes et.al (Phy. Rev. Lett, 39, pp.759, 1977) used this equation
to predict high- 
performance of tokamaks before JET was built. Stability
against low-n internal modes (fixed boundary problem, n means toroidal number of
ups and downs) can be achieved with a hollow current profile and q(0) greater than
1.63. See fig.15(a) for equlibrium diagram and fig.15(b) for stability diagram.
Figure 2: (a) Equlibrium diagram (b) Stability diagram-- From above
Notice that high- is prefered, because of efficiency use of magnetic field.
Bootstrap Current
It was predicted theoretically that pressure gradient and trapped particles can
produce parallel current in the banana region. If this current is high enough, it can
satisfy tokamak confinement conditions without external ohmic 'e' field. Bootstrap
current has been observed since middle 1980's. See fig.16 for bootstrap current
generation. 
Figure 3: Banana motion of electrons that induces the bootstrp current -- From [5]
exist 
, therefore the bootstrap current
is proportional to the parallel current:
where 
is the aspect ratio, and dp/dr is pressure gradient. It's
easy to see that the bootstrap current is naturally offset from the magnetic axis.
For detailed derivation of bootstrap current, one can refer to [5] 8.2
Reversed Magnetic Shear
From eq.(110), we can see that ballooning modes impose a constraint on the upper limit
presure gradient that can be derived which limit the value that can be used.
But from above analysis, we can see that a tokamak plasma can be stabilized under high
if the current profile is a hollow shape. Notice that
(eq.(110))
which implies that reversed magnetic shear can improve the limit, bootstrap
current and stability simultaneously.
Reversed magnetic shear has several beneficial effects. Among these are complete
stability to 
ideal MHD balooning modes in the reversed shear region. This
implies that balooning mode stability does not impose any constraint on the pressure
gradient there. It permits strong peaking of the pressure profile, which can allow a
large ratio of bootstrap current to total current, and also produce a bootstrap
current profile with favorable shape of stability. Reversed shear can also contribute
to improved plasma confinement by acting to help suppress the trapped particles
instabilities. See fig.17 for current profile in the magnetic reversed shear etc.
Figure 4: Reversed magnetic shear -- From E.J.Strait et.al.
For theoretical analysis of reversed magnetic shear, refer to J. Kesner, Phy. Lett. A,
219(1996)pp.303.
For experiments results, refer to F.M.Levinton, et.al.,Phy. Rev. Lett 75(1995)pp.4417
and E.J.Strait, Phy. Rev. Lett., 75(1995)pp.4421
For other related, refer to A.Sykes, Phy. Rev. Lett., 39(1977)pp.757 and C.Kessel,
Phy. Rev. Lett., 72(1994)pp.1212