With a $1 billion verdict hanging in the balance, feuding tech titans Apple and Samsung return to federal court armed with the latest legal ammunition in their global smartphone and tablet war.

This duel, which unfolds before U.S. District Judge Lucy Koh on Thursday, centers on Samsung’s bid to overturn a jury’s stunning verdict in August that found the South Korean tech giant “willfully” copied Apple’s iPhone and iPad in its own increasingly popular smartphones and tablets.

But Thursday’s hearing is also very much about Apple’s attempt to exact even more punishment against Samsung, its chief rival with products such as the Android-driven Galaxy line of smartphones. Apple has asked Koh to permanently ban the sale of more than two dozen Samsung devices in the United States, all of them older versions, as well as add more than $500 million to the $1 billion judgment under provisions for increasing damages for willful patent infringement.

If the judge sides with Apple, experts predict it could fuel a push by Apple to expand any injunction to cover some of Samsung’s newer smartphones and tablets, already the target of a second pending federal patent lawsuit.

For Samsung, the post-trial sparring is considered a prelude to an anticipated appeal to the U.S. Federal Circuit Court of Appeals, the Washington, D.C.-based court that hears patent cases and has thus far appeared more receptive to Samsung’s legal arguments than Koh has. For the most part, legal experts do not expect Samsung to gain much relief from the San Jose federal judge, although some speculate she may be willing to pare the damages.

“I think Samsung faces an uphill battle in persuading Judge Koh to reverse the jury verdict,” said Mark Lemley, a Stanford University law professor. “The jury obviously took its job very seriously, and even if Samsung could prevail on a few points it would need to persuade Judge Koh that the jury was wrong on multiple grounds to have much effect on the ultimate award.”

The jury concluded Samsung’s older line of products, such as the Fascinate, Epic 4G and Galaxy S II smartphones, trampled on Apple’s design and technology patents. These patents ranged from the shape of an iPhone to its “pinch and zoom” features. The jury also rejected Samsung’s counterclaims against Apple.

Samsung and Apple did not respond to requests for interviews. But both companies’ lawyers have filed stacks of legal arguments in recent months outlining their competing positions.

Among other arguments, Samsung alleges the jury’s verdict was tainted by the jury foreman’s misconduct, particularly his alleged failure to disclose that he’d been sued in the past by his former employer, Seagate Technology. Samsung, a large stakeholder in Seagate, accuses Velvin Hogan, the foreman, of deliberately omitting the information to get on the jury, and also alleges that his comments to media outlets after the verdict, including to the San Jose Mercury News, showed bias against Samsung.

Hogan declined to comment, but told the Mercury News after Samsung first raised the argument that “there was no jury misconduct.” Apple also disagreed with Samsung’s argument that Hogan’s conduct tarnished the deliberations.

Legal experts say such arguments are a long shot.

“I don’t expect Judge Koh to rule in Samsung’s favor on the jury misconduct issue,” said Brian Love, a Santa Clara University law professor. “The rules of evidence make it quite hard for a court to reverse a verdict on this basis.”

Samsung relies on other arguments to set aside the verdict, including the “manifest unfairness” of Koh’s restrictions on the amount of time each side could use to present evidence. Samsung also opposes Apple’s bid to block the sales of the products, calling it a ploy to “bully Samsung and third parties in an effort to stifle lawful, fair competition.”

Apple, however, argues Samsung deserves stiff punishment.

“Samsung copied this intellectual property in a calculated effort to wrest market share from Apple,” Apple’s lawyers wrote.

In fact, the most recent data shows Samsung’s smartphones, led by its Galaxy S III, continue to lead Apple’s iPhone in worldwide sales, while Samsung is also putting a dent in Apple’s tablet lead.

As a result, a second pending court case between the two companies promises to be the next battleground, even as Koh weighs the recent jury verdict. That case, filed earlier this year by Apple, centers on the newer line of products from both Apple and Samsung, including Samsung’s Galaxy S III phone and Apple’s iPhone 5.