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Short description of how phasers work
Energy from the power cell is modulated by three interconnected parts: the beam control assembly (the operating buttons), the safety interlock (to personalise the user) and the subspace transceiver assembly (STA)STA NOTE (which limits the power of shipboard firings unless overridden by the authority of a senior command officer). Once the energy has passed through these control mechanisms it is routed into the pre-fire chamber. It is held here until the trigger is depressed, at which point the energy is passed to the emitter crystal. There it is converted into a tuned phaser discharge and released according to the setting. Phaser type-1, which is now issued only as backup, has eight settings. The type-2 has an additional eight settings. Settings range from 'stun', which renders an organic target unconscious, 'heat' for warming objects such as rocks for use as heat or light sources, and 'disruption' which destroys objects and almost any known lifeform. Below the following diagrams is a long description of how hand phasers work.
type-2 phaser, as used by Voyager's crew in 2371 (it became Starfleet issue in 2266, in [TNG] season three).
type 2 phaser, as used by Voyager's crew 2372 onwards
Long description of how phasers work (see also the diagrams above)
Phaser fire and streamlined beam are the same, whether for ship arrays or handheld phasers.
Energy for phaser operation is stored within a replenishable sarium krellide cell. Sarium krellide holds a maximum of 1.3 x 106 megajoules per cubic centimetre, at a maximum leak rate of no more than 1.05 kilojoules per hour. The total stored energy of even the type-1 phaser, if released all at once, is enough to vaporise three cubic metres of tritanium. Accordingly there is a safety interlock (described below) within the unit that prevents, among other things, a storage cell from being discharged accidentally. Energy from the power cell is controlled by all three modules and routed by shielded conduits to a pre-fire chamber, a 1.5 cm diameter sphere of LiCu 521 reinforced with gulium arkenide. Here the energy is held temporarily by a collapsible charge barrier before passing to the actual LiCu 521 emitter for discharge out of the phaser, creating a pulse. As with Voyager's hull-mounted phaser banks, the power level set by the operator determines the pulse frequency and relative proportion of protonic charge created in the final emitter stage. The type-1 phaser contains a single pre-fire chamber, the type-2 contains four.
When the phaser's trigger is depressed, the charge barrier field breaks down in 0.02 picoseconds. Through the rapid nadion effect the LiCu 521 segmented emitter converts the pumped energy into a tuned phaser discharge. As with the ship's main phasers, the greater the energy pumped from the pre-fire chamber so the higher will be the percentage of nuclear disruption force (NDF) created. At low to moderate settings, the nuclear disruption threshold will not be crossed, limiting the phaser discharge to stun and thermal impact resulting from simple electromagnetic (SEM) effects. At the higher settings, as an override precaution for the operator, the discharge will take a distance of approximately one metre to decay and recombine to form fully-lethal emissions. In the type-1 phaser, the emitter crystal is an elliptical solid measuring 0.5 x 1.2 cm but this has developed in the type-2 phaser which Voyager's crew use to a regular trapezoid 1.5 x 2.85 cm.
Hand phasers work by applying the principle of rapid nadion effect. A rapid nadion pulse is a burst of subatomic nadion particles that facilitate a release of energy from the emitter crystal in a phaser ([TNG: The Mind's Eye]). Rapid nadions are short-lived subatomic particles possessing special properties related to high-speed interactions within atomic nuclei. Among these properties is the ability to liberate and transfer strong nuclear forces within a particular class of superconducting crystals known as fushigi-no-umi. The crystals were thus named when it appeared to researchers at Starfleet's Research & Development facility that the materials being developed were a virtual 'sea of wonder'. The effect when energy is released in this way is called the rapid nadion effect (RNE), and phasers operate on modified version of the RNE. Rapid nadions produce a pulsed protonic charge in the heart of the phaser device, a stabilised LiCu 521 superconducting crystal (lattice formula Li<>Cu> 
USS Voyager fires port-side phasers.
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Screenshots from source CC.
So no "Well, I was cleaning it and it went off" or "Whoops, where did my three metres of tritanium go?" Sarium krellide must be coupled with the LiCu 521 crystal for discharge to occur. Cell charging can be accomplished aboard shipthrough standard powertaps of the electroplasma system, and in the field through portable bulk sarium krellide units. The type-1 phaser cell measures 2.4 x 3.0 cm and holds 7.2 x 106 megajoules (megajoules, whose standard abbreviation is MJ, is a unit of energy measurement). The type-1 cell measures 10.2 x 3.0 cm and holds 4.5 x 1 01 megajoules. Downstream from the power cell are three interconnected control modules: the beam control assembly, safety interlock, and subspace transceiver assembly (STA). The beam control assembly includes tactile interface buttons for configuring the phaser beam width and intensity, and a firing trigger. The safety interlock is a code processor for making the power functions of the phaser safe and for personalising a phaser for limited personnel use. Key-press combinations of beam width and intensity controls by the operator configure the phaser's safety condition. The STA is used as part of the safety system while aboard Starfleet vessels. It maintains contact between the phaser and the ship computers to ensure that power levels are automatically restrained during shipboard firings, usually limited to heavy stun. Emergency override commands may be keyed in via the beam controls, as must have been the case when the Ilari called Tieran (while occupying Kes' body) used a phaser to kill Ensign Martin in the transporter room in [#52 Warlord]. The STA adapted for phaser use is augmented with target sensors and processors for distant aiming functions.
upper pictures: accompanied by a security team, Tuvok phasers a Klingon
lower pictures: phaser fire just misses Paris and hits his console, and Janeway opens fire
above 4 screenshots: [#160 Prophecy]
type-2 phaser, as used by Voyager's crew in 2371; this version became Starfleet issue in 2366
type-2 phaser, as used by Voyager's crew 2372 onwardsThe phaser types 1 and 2 have power levels designated 1 to 8, with the phaser type-2 having an additional eight levels up to 16 [TNG: Frame of Mind]. See Power Settings. The additional settings 9 to 16 all involve high proportions of nucleur disruption energy, with individual emitter segments capable of directing a maximum of 0.01 megawatts (by comparison, Voyager's phaser banks, i.e. the ones structurally incorporated into the ship's hull, which are Type X collimated phaser arrays, have individual emitter segments capable of directing up to 5.1 megawatts). The type-2 phaser modifications include an improved sarium-krellide power cell, curved grip, and reinforced pre-fire chamber, among others. The power cell is hot-swappable in the field and holds a total energy charge of 8.79 x 107 megajoules. The power cell is now housed within a 45° curved grip for improved targeting and handling. Within the optronics and energy-manipulation section, the lithium-copper pre-fire chamber has been strengthened with the addition of a wound hafnium tritonide fibre layer, which allows a pre-fire chamber energy density and plasma pressure 15% higher than that of the previous type-2 unit. Control surfaces, response, and operation remain unchanged. 
type-2 phaser, as used by Voyager's crew from 2372 onwards:
left: with hip-holster right: service configuration
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