What was found
AIR TURN BACK DUE TO CREW NOTICED ARCHING IN THE LH WINDSCREEN AT FL410. SHORTLY AFTER, A SMELL OF BURNING ELECTRICAL WIRES WAS NOTICED AND THE LH WINDOW HEAT WAS DEACTIVATED. FOLLOWING THIS, A LOUD POP WAS HEARD, AND THE WINDSCREEN CRACKED. CREW FOLLOWED CHECKLIST AND TURNED BACK TO LAX AT PASSENGER REQUEST. AIRCRAFT LANDED WITHOUT INCIDENT. REPLACED LEFT HAND WINDSHIELD ASSEMBLY IAW G650 AMM 56-11-01. OPS AND LEAK CHECK SATISFACTORY.