BOSTON (AFP) - Boston bomber Dzhokhar Tsarnaev is "America's worst nightmare" and deserves to die for one of the bloodiest attacks on US soil since 9/11, his trial heard Tuesday.

The court was shown a never-before seen photograph of Tsarnaev, dressed in an orange prison jumpsuit flipping his middle finger at a surveillance camera in a cell before his first arraignment.

"This is Dzhokhar Tsarnaev, unconcerned, unrepentant and unchanged," said assistant US attorney Nadine Pellegrini in her opening statement at the penalty stage of his trial.

The former student was convicted earlier this month on all 30 counts related to the April 15, 2013 bombings, the murder of a police officer, a carjacking and a shoot out.

The 21-year-old of part Chechen descent who moved to America with his family aged eight took US nationality a year before the deadly 2013 attacks, which killed three and wounded 264 more.

"The death penalty is appropriate because Dzhokhar Tsarnaev planned and plotted to kill," Pellegrini told jurors. "His character makes the death penalty appropriate."

She also displayed large colour photographs of the victims, looking happy and well, before they were killed.

The "unbearable, indescribable, inexcusable, senseless" attacks, she said, proved Tsarnaev and his twisted, extremist ideology were "destined to become America's worst nightmare."

"He shared his beliefs in terrorism with his brother," 26-year-old Tamerlan who was killed by police while on the run, and "the people in the crowd were his enemies," she said.

Tsarnaev, who while on the run said the attacks were revenge for the US wars in Iraq and Afghanistan, sat between his female lawyers not looking at Pellegrini, dressed in a black blazer and dark pants.

The federal court room was packed for the first day of the penalty phase, which began with instructions from the judge to the jury, the same 12-member panel that convicted Tsarnaev on April 8.

"Obviously it is impossible for me to overstate the importance of the decision," Judge George O'Toole told jurors.

Outside the building, a dozen protesters demonstrated against the death penalty, holding up banners, one of which read: "Why do we kill people who kill people to show that killing people is wrong?"

Jurors were selected in part for their openness to imposing the death penalty, controversial in a state that has executed no one since 1947 and where Catholic bishops oppose capital punishment.

The sentencing decision has to be unanimous. If just one juror accepts there were mitigating circumstances to Tsarnaev's actions, then he will be sentenced to life in prison.

Double amputee Celeste Corcoran was the first to testify for the prosecution on Tuesday, recalling a beautiful day before the bombs wrought carnage and the terrible pain she endured.

The penalty phase, which is expected to last three to four weeks at the federal court in the northeastern US city, will see both prosecutors and defence attorneys call witnesses.

It is unclear whether Tsarnaev, who has been a silent if fidgety presence in court, or any of his relatives will take the stand.

His parents now live in Russia, although his two sisters and Tamerlan's widow, a US-born Muslim convert, live in the United States.

Prosecutors will try to convince the 12 jurors that there are enough aggravating factors - including premeditation, the number of victims and a lack of remorse - to warrant capital punishment.

The defence will argue their client should be sent to prison, portraying him as a confused 19-year-old, frightened of his more radical, older brother.

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