To　suppress　the　secondary　electron　multipactor　on　dielectric　surfaces　of　a　dielectric　load　accelerator　under　an　electromagnetic　field　in　TM　mode,　the　method　of　adopting　both　groove　structure　and　external　axial　magnetic　field　is　introduced.　As　the　electric　field　distribution　of　the　TM　mode　is　composed　of　both　normal　and　tangential　components,　it　is　different　from　that　under　the　condition　of　dielectric　window　in　HPM.　Thus,　theoretical　analysis　and　numerical　simulation　are　employed　to　study　the　movement　of　electrons　under　different　conditions:　such　as　dielectric　surface　shapes,　electric　field　strength,　and　magnetic　field　strength　etc.　Based　on　the　particle-in-cell　(PIC)　simulation,　the　collision　energy　and　transmit-duration　of　secondary　electrons　in　different　groove　structures　and　axial　magnetic　fields　are　compared　with　one　another.　Results　show　that　the　magnetic　field　is　useful　for　suppressing　the　development　of　secondary　electron　on　dielectric　surface,　while　it　is　not　very　efficient　under　high　electric　field　strength.　The　method　of　introducing　groove　structure　and　certain　axial　magnetic　field　on　dielectric　surface　at　the　same　time　is　capable　of　affecting　the　movement　of　electrons　in　electric　field　of　different　strength.　So　it　is　great　helpful　in　improving　the　ability　of　multipactor　suppression,　which　is　significant　for　improving　the　threshold　of　breakdown　on　dielectric　surface　and　the　power　of　cavity.　However,　a　too　high　or　too　low　magnetic　field　is　not　very　useful　for　the　suppression　of　multipactor.　Furthermore,　employing　only　one　of　the　two　parts　of　the　method　is　also　less　effective　in　suppressing　the　multipactor.