The inhomogeneous electron cloud in atomic ions ‘confined’ in hot plasmas and subjected to high static electric fields is studied, because of a body of experimental data on multiphoton ionization. In particular, the canonical (Bloch) density matrix is obtained in closed form for independent electrons moving in a static electric field of arbitrary strength and confined by a harmonic oscillator potential. To bring the model into contact with atoms in plasmas, the oscillator force constant is connected with the plasma density. For non-degenerate electrons an ‘atomic’ potential is included, by means of the Thomas—Fermi (TF) method. In an Appendix, a fully non-local theory is then developed which transcends this TF approximation. Simple numerical examples are presented for realistic values of field, temperature and plasma density.