A fuel injection system for use in a self-igniting internal combustion engine which defines a cylinder containing a reciprocating piston and which provides a combustion chamber, said fuel injection system comprising an injection valve for direct fuel injection of liquified gases into said combustion chamber, said injection valve including a housing defining a discharge nozzle, a fuel needle located in said housing and having a pintle tip that moves up to about 1 mm relative to said nozzle to close said nozzle or to open said nozzle to provide a throttled fuel flow therethrough, a spring located within said housing to bias said fuel needle into a closed position relative to said nozzle, and an electromagnet means for directly applying a force on said fuel needle to lift said fuel needle against said bias of said spring and lift said fuel needle so as to open said nozzle, magnetic force from said electromagnet means increasing quadratically with lift of said needle against a linearly increasing bias force of said spring, resulting in an approximately quadratically increasing opening velocity of said fuel needle in certain regions to permit small pintle lift, wherein said electromagnet means comprises a solenoid, wherein said fuel needle includes a generally disc-shaped end portion which is spaced from said solenoid, and wherein said spring extends within said solenoid to abut said disc-shaped end portion to bias said end portion in spaced relation to said solenoid.