MHD generators have difficult problems in regard to materials, both for the walls and the electrodes. Materials must not melt or corrode at very high temperatures. Exotic ceramics were developed for this purpose and must be selected to be compatible with the fuel and ionization seed. The exotic materials and the difficult fabrication methods contribute to the high cost of MHD generators.
Also, MHDs work better with stronger magnetic fields. The most successful magnets have been  superconducting, and very close to the channel. A major difficulty was refrigerating these magnets while insulating them from the channel. The problem is worse because the magnets work better when they are closer to the channel. There are also severe risks of damage to the hot, brittle ceramics from differential thermal cracking. The magnets are usually near absolute zero, while the channel is several thousand degrees.
For MHDs, both alumina (AlO) and magnesium peroxide (MgO) were reported to work for the insulating walls. Magnesium peroxide degrades near moisture.  Alumina is water-resistant and can be fabricated to be quite strong, so in practice, most MHDs have used alumina for the insulating walls.
For the electrodes of clean MHDs (i.e. burning natural gas), one good material was a mix of 80% CeO, 18% ZrO, and 2% TaO.
Coal-burning MHDs have intensely corrosive environments with slag. The slag both protects and corrodes MHD materials. In particular, migration of oxygen through the slag accelerates corrosion of metallic anodes. Nonetheless, very good results have been reported with stainless steel electrodes at 900K. Another, perhaps superior option is a spinel ceramic, FeAlO - FeO. The spinel was reported to have electronic conductivity, absence of a resistive reaction layer but with some diffusion of iron into the alumina. The diffusion of iron could be controlled with a thin layer of very dense alumina, and water cooling in both the electrodes and alumina insulators.
Attaching the high-temperature electrodes to conventional copper bus bars is also challenging. The usual methods establish a chemical passivation layer, and cool the busbar with water.