Magnetic Fields Parallel to the Helix Axis

We will first consider a planar chiral sample with a magnetic field H applied across the sample along the z or the initial helix axis direction. The diamagnetic susceptibilities are defined as X and x i-e., parallel and perpendicular to the local director. Since n spirals around z (see Eq. 1), this gives a value of x parallel to H and iXw+Xx) orthogonal toH. If li Xi=X X ) 

For an unperturbed planar chiral nematic with the helix along z, the director is given by Eq. (1). If we now assume small perturbations in 0 and that the director layers undulate sinusoidally by an amplitude 9 (see Fig. 32), we have 

Equation (2) then gives the local energy density Fi as 

The minimum energy density )3 is then I (3fe33 + fe22)g Q kqx i 

Under these approximations, the free energy density, taking into acount undulations, 

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