In this brief note, we correct typographic errors in ‘Stepped pressure profile equilibria in cylindrical plasmas via partial Taylor relaxation [J. Plasma Physics (2006), vol. 72, part 6, pp. 1167–1171].’ Equation (3.2) is in error and should read

In general, however, $Y_0 (u), Y_1(u)$ are complex numbers when $u$
is a negative real number. To ensure the field is physical for real $k$
and $d$
coefficients, it is more consistent to write the solution for both region 1 and region $i$
as


With this modification, (3.7) and (3.8) become


The equilibrium is specified by $4N+1$ parameters, not $4N+2$
as stated in the paper.
The parameters provided for figure 1 are incorrect, and should read $r_w=1.5, B_{V,\theta }= 0.2362, B_{V,z}= 0.4000, r_i=\{0.2, 0.4, 0.6, 0.8, 1.0\}, $ $\mu _i= \{ 1.5,1.3,1.1,1.0,0.8\}, k_i = \{0.2229,\ 0.2538,\ 0.2894,\ 0.3086,\ 0.3506 \},$
$d_i = \{0,\ -0.0021,\ -0.0102,\ -0.0191, -0.0495\}$
. These parameters were obtained by solving for $k_i$
and $d_i$
such that $\mathbf {J}_{i+1} - \mathbf {J}_i$
evaluated at the interface was zero, and so $q_i^i = q_i^o$
. The procedure was as follows. In the core region, $\mu _1, k_1, d_1$
is given, and so $\mathbf {J}_1(r_1)$
can be computed. We have next solved $\mathbf {J}_1(r_1) = \mathbf {J}_2(r_1) = \mu _2/\mu _0 \mathbf {B}_2(r_1)$
for $k_2, d_2$
, which gives $\mathbf {J}_2(r_2)$
. The procedure is marched out towards the edge. At the plasma–vacuum interface, we have solved $q_i^i = q_i^o$
for $B_{V, \theta }$
.