Magnetic　interaction　between　magnetic　particles　is　of　great　significance　in　the　fields　of　magnetic　separation　and　functional　materials.　A　good　understanding　of　interaction　mechanism　of　magnetic　particles　would　further　boost　its　promising　industrial　applications.　We　hereby　present　our　work　which　visualizes　the　movement　behavior　of　magnetic　spheres　in　magnetic　fields　employing　high-speed　imaging　and　simulates　the　dynamic　behavior　of　spheres　using　an　Arbitrary　Lagrangian-Eulerian　(ALE)　based　on　finite　element　method.　In　this　paper,　we　investigated　the　stress　tensor,　magnetic　force,　and　dynamic　behavior　of　magnetic　spheres　in　magnetic　fields,　especially　magnetic　energy　density　in　different　domains.　Results　show　that　there　are　four　relatively　independent　regions　of　magnetic　energy　density　distribution　in　external　spatial　domains　of　a　single　sphere　system.　Attractive　force　will　generate　when　the　energy　density　in　the　spatial　region　between　two　spheres　is　relatively　high,　while　a　repulsive　force　will　generate　when　the　energy　density　in　the　spatial　region　between　two　spheres　is　relatively　low.　Every　magnetic　sphere　spontaneously　moves　towards　the　region　with　high　energy　density　and　stays　away　from　the　region　with　low　energy　density.　The　total　magnetic　energy　in　magnetic　spheres＇　domains　(V1)　and　external　spatial　domains　(V2)　increases,　but　the　magnetic　energy　in　the　external　spatial　domain　decreases　over　time　during　the　aggregation　process.　The　magnetic　spheres　ultimately　arrange　in　chain-like　structures　oriented　along　magnetic　field　direction.　We　hereby　proposed　a　novel　and　efficient　approach　to　predict　the　movement　trends　and　final　state　of　magnetic　particle　swarm　from　the　view　of　energy　density.　(c)　2022　Published　by　Elsevier　B.V.　on　behalf　of　China　University　of　Mining　&　Technology.　This　is　an　open　access　article　under　the　CC　BY-NC-ND　license　(http://creativecommons.org/licenses/by-nc-nd/4.0/).