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

(1)\begin{equation} B= \{0, k_i J_1 (\mu_i r) + d_i Y_1 (\mu_i r), k_i J_0 (\mu_i r) + d_i Y_0(\mu_i r)\}. \end{equation}

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

(2)\begin{gather} B = \{0, \mathrm{sign}(\mu_1) k_1 J_1 (|\mu_1| r), k_1 J_0 (|\mu_1| r)\}, \end{gather}

(3)\begin{gather}B = \{0, \mathrm{sign}(\mu_i) \left ( { k_i J_1 (|\mu_i| r) + d_i Y_1 (|\mu_i | r) } \right ), k_i J_0 (|\mu_i| r) + d_i Y_0(|\mu_i| r)\}. \end{gather}

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

(4)\begin{gather} \varPsi_i^t = \int_{r_{i-1}}^{r_i} B_z(r) r d \theta dr = \frac{2 {\rm \pi}} {|\mu_i|} \left [ { k_i r J_1 (|\mu_i| r) + d_i Y_1 (|\mu_i| r) } \right ]_{r_{i-1}}^{r_i}, \end{gather}

(5)\begin{gather}\varPsi_i^p = \int_{r_{i-1}}^{r_i} B_z(r) L dr = - \frac{L \mathrm{sign}(\mu_i)} {|\mu_i|} \left [ { k_i r J_0 (|\mu_i| r) + d_i Y_0 (|\mu_i| r) } \right ]_{r_{i-1}}^{r_i}. \end{gather}

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 $B_{V, \theta }$.