The Psychic Amplifier acts as a continental Mind-Control Device while also boosting the range of nearby Psychic Beacons little by little. It is an upgraded version of a Psychic Beacon in a way, though it requires much more time and power to activate.
In most missions where the Psychic Amplifier appears, it is a primary objective. Furthermore, a time limit will be set for the player to stop it (or defend if playing as Epsilon) before it activates. The countdown is longer than that of the Psychic Beacon.
The only Psychic Amplifier seen in the Third Great War is deployed in the city of Chicago, and its destruction is the objective of Beautiful Mind. Once it's destroyed, a MIDAS rocket will launch, destroying the city, exterminating the Soviet survivors and the entire American army.
In Puppet Master, the Roman Psychic Amplifier is the primary target of the player's European task force. The Europeans are protected from the Amplifier by a recalibrated Psychic Beacon in their base. If enough time passes after the Russians are freed by the destruction of the Beacon controlling them and the Amplifier is still standing, they'll be mind controlled again by the Amplifier. If the European Beacon is destroyed while the Amplifier is still standing, the player will be given 30 minutes to destroy the Amplifier before the Europeans succumb to it, but to compensate, the player will receive six money crates and four Spies.
Firewalking is a three-way fight between the PsiCorps, the Americans and the player's Latin Confederation over a Psychic Amplifier newly established by PsiCorps. It must be captured by the Confederation before the Americans can do so and the PsiCorps can activate it.
At the beginning of Obsidian Sands, Yuri attempts to mind control the Scorpion Cell traitors with a Psychic Amplifier. It gets quickly destroyed by the rebels, forcing him to resort to brute force. After the mission, a Psychic Amplifier was built where Rashidi's Palace stood, but was destroyed by the Paradox Engine.
In Paranoia, a Psychic Amplifier has been detected in the Amazons alongside two Tactical Nuke Silos which must all be neutralised by Tanya and Norio. The Amplifier must be destroyed after both nukes are, or else its destruction will cause a nuke to be launched at the Weather Controller in response.
In the Covert Ops mission Nightcrawler, Rahn and other Epsilon forces is required to reactivate an abandoned Psychic Amplifier to control the Scorpion Cell traitors in Africa.
Shortly before the start of the Covert Ops mission Brothers in Arms, Epsilon has established a Psychic Amplifier in the city of Stalingrad and used it to control the local Chinese and Russian forces. When the main Soviet army arrives, they have 60-80 minutes to destroy the Amplifier before it mind controls them; its destruction will also free Epsilon's Chinese and Russian slaves.
A Psychic Amplifier is mentioned to be located in Moscow.
In The Cardinal, two Proselytes must secure St. Peter's Square in the Soviet-controlled city of Rome so a Psychic Amplifier could be constructed there. It must then be defended from the Soviets until they succumb to its effects.