This　study　focuses　on　a　magnetically　stabilized　gliding　arc　(MGA)　plasma.　Two　fully　coupled　flow-plasma　models　(in　3D　and　2D)　are　presented.　The　3D　model　is　applied　to　compare　the　arc　dynamics　of　the　MGA　with　a　traditional　gas-driven　gliding　arc.　The　2D　model　is　used　for　a　detailed　parametric　study　on　the　effect　of　the　external　magnetic　field.　The　results　show　that　the　relative　velocity　between　the　plasma　and　feed　gas　is　generated　due　to　the　Lorentz　force,　which　can　increase　the　plasma-treated　gas　fraction.　The　magnetic　field　also　helps　to　decrease　the　gas　temperature　by　enhancing　heat　transfer　and　to　increase　the　electron　number　density.　This　work　shows　the　potential　of　an　external　magnetic　field　to　control　the　gliding　arc　behavior,　for　enhanced　gas　conversion　at　low　gas　flow　rates.　©　2020　IOP　Publishing　Ltd.