## 1 Introduction  
The Algerian Sahara is one of the hottest areas in the world [1]. It is characterized by its extreme desert climatic conditions and diversified topographical nature, which support the adaptation and growth of various medicinal plants [2]. The Saharan population uses these medicinal plants as an essential source of traditional remedies for the prevention of diseases because they contain various bioactive compounds. However, many of them still remain to be explored [3] and are little recognized worldwide. Increased attention has been given to these medicinal plants due to their richness in secondary metabolites, especially phenolic compounds [4, 5, 6], which exhibit several biological activities for human health, such as antioxidant [7, 8, 9], antimicrobial [10, 11], antiviral [12], anti-inflammatory [13, 14],anti-diabetic [15; 16], and anti-carcinogenic activities [13; 17]. Furthermore, these natural substances are highly recommended as an alternative to toxic synthetic antioxidants [18]. Chenopodiaceae is the ancient denomination given to plants of the Amaranthaceae family. It includes about 102 genera and 1400 species, most of which are halophytic plants distinguished by their tolerance to environmental stress and their adaptability to saline conditions [19; 20]. They are also recognized for their richness in bioactive molecules, such as phenolic acids, flavonoids, betalain pigments, saponins, essential oils [21], glucuronides, glycosides, sesquiterpenes, diterpenes, and triterpenes [19]. _Cornulaca monacantha_ Del. is a medicinal plant of the Chenopodiaceae family, noted as \"Had\". It is widely used to treat liver-related disorders and jaundice [22; 23; 24]. _Anabasis articulata_ (Forssk.) Moq. is a medicinal plant from the same family [25]. Its local name is \"ajrem\" [26]. It is widely used in Algerian therapeutic traditions to prevent the risk of diabetes and to treat kidney infections, headaches, fever, and skin diseases, especially eczema [19; 20; 27]. The extraction of bioactive substances is a primary step and a fundamental operation in separating and identifying phenolic compounds from a plant matrix [13; 15; 28; 29; 30; 31]. Generally, different extraction methods exist [32]. Nevertheless, conventional extraction methods have the disadvantages of needing long processing times and high extraction temperatures [33], and delivering low yields [34]. In response, scientists have focused on developing new and innovative green technologies that can be adopted to overcome the limitations of conventional techniques by proposing alternative methods, such as ultrasonic-assisted extraction [35; 36; 37], microwave-assisted extraction [38; 39; 40], enzyme-assisted extraction, high-pressure-assisted extraction [40], and supercritical fluid extraction [41]. Recently, ultrasound-assisted extraction (UAE) has been successfully applied to extract bioactive compounds from different plant samples [42; 43; 44], using frequencies above 20 kHz [34; 45]. It is a simple and inexpensive method used in the pharmaceutical and food industries [46]. Ultrasound-assisted extraction (UAE) reduces energy consumption by decreasing extraction time [47], reducing applied temperature [46], and decreasing solvent consumption [48; 49; 50], while improving extraction yield [44; 51]. Its mechanism of action consists of transforming electrical or mechanical energy into acoustic waves through a transducer [52]. These waves propagate through the container medium as sound waves in successive cycles of compression and rarefaction [53; 54]. This propagation mode leads to the appearance of the cavitation phenomenon and the creation of microbubbles inside the plant cells [53; 55]. These microbubbles collapse into a bubble at or near the surface of the cell wall and then implode under the primary physical effect of shear force [46; 56; 57] and under the secondary chemical and thermal effects [44; 58], causing the rupture of the cell wall and the mass transfer of its contents into the surrounding extraction medium [9; 45; 59; 60; 61].