It has been known that the width of the trapped particles, i.e. bananas, is reduced or squeezed in a magnetic well in tokamaks. The magnetic squeezing factor SB depends on the energy and pitch angle of the particles. When ρp/a ∼ 1, SB becomes appreciably larger than unity; it can be of the order of 2 for a parabolic well with B−1 d2B/dr2 ∼ 2a−2. Here, ρp is the poloidal gyro-radius, B is the magnetic field strength, r is the local minor radius, and a is the minor radius. However, the real orbit width measured in terms of the poloidal magnetic flux is still less than a because of the magnetic squeezing; for SB = 2, it is a 30% reduction. The transport consequences of the squeezed bananas in a magnetic well are calculated by solving the drift kinetic equation utilizing the constants of motion in the large aspect ratio limit. Consequently, neoclassical ion heat conductivity χh in the reactor relevant collisionality regime (i.e. banana regime) is reduced by a factor of ; for SB = 2, it is almost a factor of three reduction for the same temperature. The ion temperature scaling of χh improves from the conventional, and weakly favorable scaling to the strongly favorable scaling for high temperature fusion grade tokamak plasmas; the scaling however does not take the temperature dependence of the magnetic well itself into account. Here, Ti is the ion temperature. In addition, it is shown that plasma turbulence is suppressed in a magnetic well using the reduced decorrelation time argument and anomalous plasma confinement is improved. The combined improvements result in a favorable temperature scaling in the ion energy confinement time, and make burning aneutronic fuels feasible. The implications on a tokamak with a magnetic well as a fusion reactor are discussed.