Plasma automatically impacts the target unless dealt with using one of the methods noted in the rules, so at half range all 7 dice would strike the target (no roll to hit, so no chance to bypass shields).
As the weapon has the Multihit D6 trait, you'd roll 7xD6 and apply that number of hits to the target's shields. Hits in excess of the current shield value strike the hull and each one is rolled for on the Attack Table on p7 of the rulebook, just like hits from direct fire weapons.