It is shown that the Debye length formulation, for plasmas described by kappa distributions, depends on the polytropic index, rather than the parameter that labels and governs these distributions, the kappa index—in contrast to what it was previously derived. As a consequence, the ratio of the Debye length over the plasma oscillation period gives exactly the sound speed, instead of being proportional to the thermal speed; this ratio is generalized to the fast magnetosonic speed when the magnetic Debye length is considered, leading also to the development of the vector Debye length. Finally, as an application, we derive the Debye length values for the solar wind plasma near 1 AU, exhibiting clear distinction between slow and fast wind modes, while we provide insights into the connection between plasma and polytropic processes.It is shown that the Debye length formulation, for plasmas described by kappa distributions, depends on the polytropic index, rather than the parameter that labels and governs these distributions, the kappa index—in contrast to what it was previously derived. As a consequence, the ratio of the Debye length over the plasma oscillation period gives exactly the sound speed, instead of being proportional to the thermal speed; this ratio is generalized to the fast magnetosonic speed when the magnetic Debye length is considered, leading also to the development of the vector Debye length. Finally, as an application, we derive the Debye length values for the solar wind plasma near 1 AU, exhibiting clear distinction between slow and fast wind modes, while we provide insights into the connection between plasma and polytropic processes.