(CBS) Terror suspect Jose Padilla brought al Qaeda officials “laughably inaccurate” instructions to make a hydrogen bomb and was urged to focus on a conventional explosive combined with radioactive material, Time magazine reported Sunday.

Padilla, the alleged “dirty bomb” plotter, reportedly came across the hydrogen bomb plans on the Internet and presented them earlier this year to al Qaeda staff including Abu Zubaydah, Osama bin Laden's operations chief, the magazine said. Zubaydah is currently in the custody of the United States.

Senior Bush administration officials told Time that Padilla, an American citizen, expressed interest in setting off such a weapon on American soil. But the al Qaeda bosses told him to think smaller.

“They sent him to the U.S. to see what he could do - plan and execute,” the official was quoted as saying.

Padilla, 31, was arrested in Chicago when he got off a plane from Pakistan on May 8. He was brought to New York and then moved to a South Carolina naval brig on June 9. U.S. officials said the New York native, who goes by the name Abdullah al Muhajir, had been declared an “enemy combatant.”

Padilla allegedly traveled to Afghanistan several times after the Sept. 11 attacks to meet Zubaydah, who was arrested in Pakistan in March and later moved to the United States.

Such a “dirty bomb” would combine a conventional explosive with radioactive material so as to spew radiation over a large area. Such a bomb could present a serious health threat, or it could simply present logistical problems and widespread fear, depending on the lethality of the charge and any radioactive material.

Time said the arrest indicates that al Qaeda may be turning to “irregulars” such as Padilla and accused shoebomber Richard Reid to carry out attacks instead of highly trained and disciplined people like those responsible for the Sept. 11 attacks.

Reid, a British citizen, is charged with trying to blow up American Airlines Flight 63 from Paris to Miami with bombs in his shoes on Dec. 22.